Short Answer
Municipalities and many kinds of special districts are created by property owners, usually led by a real estate developer, not approved by state government except with a general authorizing statute, or by county government. Others are joint ventures by existing local governments, or are created to serve only part of the territory of an existing local government at the expensive of the property owners in that territory.
Usually, they are used to make capital investments with tax free municipal bond financed debt, often paid for with user fees or with property taxes from a very specific development's property owners who benefit from the capital improvement. This is done in a way that leaves them with very little authority and discretion outside their narrow specific function. Also, often their boards of directors are appointed rather than elected.
Developers have disfavored general purpose municipal government over special districts in recent times, even though this means that more governmental entities are needed. In part, this is due to a distaste for the taxing and regulatory authorities of municipalities (especially their land use regulation authority). In part this is because modern constitutional case law imposes limitations on what governments can do causing developers to prefer private home owner's associations for ends that are constitutionally regulated. In part, this is because they can create a special district government without approval from local elected officials in general purpose governments who may want to extract concessions in order to allow for new development.
Special districts are also useful when public works that cross local government boundaries or only impact a small area within a government's boundaries, like a drainage system, need to be built and financed.
To some extent, the trend towards special districts and away from general purpose municipalities reflects a distrust of the democratic process and a declining sense of shared benefit and obligations in larger communities.
Long Answer
Overview
Illinois has 102 county governments, 1,299 municipal governments, 1,426 township governments, 852 school district governments, and a very large number of special district governments.
Counties
All land in Illinois is in a county. County governments are locally elected bodies that mostly carry out state government functions like property tax collection, operating courts, and providing law enforcement in areas outside municipalities.
Counties have limited tax collection authority and can only provide select services.
Townships
Almost all land in Illinois is in a township. Township governments are (approximately and with one or two exceptions) thirty-six square mile administrative divisions whose main responsibility is to maintain local roads in 85 counties (but 17 counties don't have township government and there is also no township government in the Cities of Chicago and Cicero despite the existence of township government in the rest of the counties where those cities are located). In counties without separate township governments, these functions are handled by county government. Five townships in Illinois have been merged into other governments or dissolved since 1987 and these are part of the discrepancy between the lists:
The differences in the total number of general-purpose governments by
each reporting agency is minimal and due to the inclusion of townships
and municipalities that are no longer in existence or how they are
classified. For example, the U.S. Census Bureau and Illinois
Department of Revenue include Belleville Township, while the Illinois
Comptroller no longer lists Belleville Township since it was dissolved
in 2017. Also, the Illinois Comptroller’s listing of local governments
was the only reporting agency that still included the Village of
Whiteash in Williamson County, which voters dissolved in 2014. As
another example, the U.S. Census Bureau includes South Fillmore
Township in Montgomery County separately even though it merged with
Fillmore Township to create Fillmore Consolidated Township. Also, the
Illinois Department of Revenue classifies the Town of Cicero in Cook
County as a township, while the Illinois Comptroller and U.S. Census
Bureau classify it as a municipality.
In the New England model, town governments provided municipal government functions and also carry out some of the functions of county government in other states for the entire territory of a state. Also, historically, New England towns operated on something approaching a direct democracy basis, with town meetings held periodically constituting their ultimate source of governing authority.
Townships were originally envisioned on the New England model, but in the Midwest, which was much more sparely populated in rural areas, township government devolved into its much diminished current form. Some urban townships in the Midwest, however, carry out additional functions similar to those of municipalities in areas outside municipal governments.
For example, the place called the City of Cicero in Illinois is, strictly speaking, organized in terms of governmental structure as a township rather than as a municipality, despite its name.
School Districts
All land in Illinois is in a school district. School districts operate local public schools up through 12th grade, and sometimes publicly funded trade schools for students of high school age, in a geographically defined district, mostly with a mix of local property tax and state grant funding. The U.S. norm is for public schools to be governed by separately elected boards rather than being part of another government. They are further regulated by a state board of education and typically have only minimal power to raise taxes or incur debt without first obtaining voter approval. The number of school districts in Illinois has fallen by about 200 since 1987 as smaller school districts have consolidated for economies of scale.
Municipal Governments
Municipal governments are created (mostly) by a petition to a court supported by local property owners and usually led by a real estate developer supporting incorporation of a municipality. Municipal governments are rarely created now, because municipal governments are subject to constitutional law limitations as governments and because they can unilaterally impose taxes without voter approval, and because they can regulate land use with zoning laws and building codes. Instead, developers now prefer to create a private homeowner's association (sometimes with a master association for an entire development and local ones for different parts of the development like condominium buildings) and to create specific special districts to carry out functions that municipal governments would otherwise provide that a homeowner's association is ill-suited to provide.
Only 20 municipal governments have been created since 1987 in Illinois.
Special District Governments
Most special district governments are also not approved by state government at some point in time. Instead, they are mostly created by an application to a court supported by a petition of land owners to create one, usually led by a real estate developer. About 460 special district governments have been created in Illinois since 1987. Most of the general authorizing statutes are here.
For example, to create a drainage district, which follows a typical special district formation process, one must start with a petition:
A drainage district may be organized upon petition signed by 20% of
the adult owners owning more than one-fourth of the land in the
proposed district; or by more than one-fourth of the adult owners
owning a major portion of the land. When the land in the proposed
district is owned by 2 owners only, the petition need be signed by
only one owner if he owns at least one-fifth of the land in the
proposed district. The petition shall be filed in the circuit court of
that county in which the greater part of the land shall lie. It must
include: (a) the name of the proposed district; (b) a statement
showing the necessity for the district; (c) a general description of
the proposed work; (d) a general description of the location of the
lands in the proposed district or the numbers of the sections,
including township and range, in which the proposed district, or any
part thereof, is situated; (e) the names of the owners, when known;
(f) the approximate number of acres in the proposed district; (g) a
request for the organization of the district; and (h) a request for
the appointment of temporary commissioners.
The petition is then set for a court hearing at which the court makes the following determinations:
At the hearing, the court shall determine whether or not the requisite
number of owners owning the required acreage of land signed the
petition or joined as petitioners. The affidavit of one or more
credible persons may be taken as prima facie evidence of the
sufficiency of the signing of the petition. Any owner of land situated
within the proposed district may, at or prior to the time fixed for
hearing, file objections to the sufficiency of the petition on the
ground that it does not fulfill the requirements of Section 3--3, and,
after filing such objections, may be heard with reference thereto and
introduce evidence thereon.
The court has very few grounds upon which it can refuse to form the drainage district:
If the court finds that the petition has not been signed as required
by Section 3--3 or that the petition does not otherwise fulfill the
requirements of Section 3--3, it shall dismiss the petition at the
petitioners' costs. If the court determines that the petition has been
properly signed and otherwise fulfills the requirements of Section
3--3, it shall find for the petitioners.
No other unit of government has standing or grounds to object to the formation of the drainage district. And, while it isn't obvious that this is the case, usually a drainage district or other special district petition will be filed concerning land with a single owner, typically a large subdivision developer which has not yet sold off individual lots. And as the link in the original question notes:
there are smaller special purpose governments included that are
sometimes very small in geographical size that are still in existence
and may still provide services, but the entire local government may be
governed and operated by one person. These instances occurred
primarily with drainage districts.
The Civic Federation count of local governments includes 2007 entities with appointed boards that are entirely within the territory of the government that appoints their board that are treated as "subordinate agencies" by the U.S. Census Bureau, the Illinois State Controller, and the Illinois Department of Revenue (mostly the 1,391 road and bridge districts and 79 road districts and 334 multi-township tax assessment districts in the state of Illinois). These entities are basically township level subdivisions or intergovernmental agreements for matching property taxes to road and bridge financing costs as the link in the question explains:
The U.S. Census Bureau excludes governments that lack several
characteristics, namely fiscal and administrative autonomy. As result,
road and bridge districts, which are frequently classified as
divisions of townships, are not included in the Census Bureau’s
listing of local governments or the Illinois Department of Revenue’s
listing 6. However, the Illinois Comptroller’s registry of local
governments recognizes road and bridge districts as a separate type of
local government. For the purposes of the report, the Civic Federation
also lists road and bridge districts separately from townships because
not all townships have road districts and/or road and bridge
districts. There are several types of road districts allowed under
Illinois state law. Certain road districts are consolidated districts
that include two or more townships. There are also municipal road
districts that are solely within the boundaries of a municipality and
unit road districts that are typically governed by the county board.
The 2017 Census of Governments listing also does not include
multi-township tax assessment districts, which accounts for
approximately 325 additional units of local government. Multi-township
tax assessment districts are responsible for the assessment of real
property in townships with a population less than 1,000 residents and
other townships electing to use these provisions.
There are myriad kinds of special districts in Illinois including: airport authorities, cemetery maintenance districts, the Chicago Transit Authority, civi center authorities, conservation districts, drainage districts, fire protection districts, hospital districts, housing authorities, the Interstate Bridge Commission, the metropolitan exposition, auditorium and office building authorities (at least nine of them), metropolitan fair and exposition authorities, mosquito abatement districts, park districts, port and regional port districts (at least 13 of them), public building commissions, public library districts, regional transportation authorities, river conservancy districts, sanitary districts (three kinds), school finance authorities, soil and water conservation districts, solid waste disposal districts, street lighting districts, surface water protection districts, transit districts, tuberculosis sanitarium districts, and water supply districts. See also here with pretty pictures.
A few have elected boards of directors (including some in which property owners may vote even if they are not natural persons or are not U.S. citizens or are not adults), but most have boards of directors appointed by other local governments. Some have property taxation powers, while others are supported only by state and federal grants or by user fees.
Almost all special districts issue municipal bonds to make public sector capital investments that are preferred over private sector financing of the same capital investments, because municipal bonds are tax free and as a result can be issued with lower interest rates than corporate bonds that reflect the tax savings received by municipal bond investors in high tax brackets.
Special districts are often preferred over having a private homeowner's association provide a function due to their capacity to issue municipal bonds. They are often preferred over municipalities because of a distrust of government growth and "mission creep" since they can only perform one or two very specific functions. Special districts have limited taxing and borrowing power without voter approval, and they don't have law enforcement or land use regulation authority. Special districts also more precisely match taxes for public works to the people who benefit from them.
Soil and water conservation districts have boundaries that closely match county lines, and exist primarily to implement federal grant programs in a manner prescribed by state government, at a local level.
