For a two-part question, you get a two-part answer.
Tax Freedom Day
Tax Freedom Day is a fairly straightforward calculation.
We count in the denominator every dollar that is officially part of national income according to the Department of Commerce’s Bureau of Economic Analysis, and in the numerator every payment to the government that is officially considered a tax is counted. Taxes at all levels of government are included, whether levied by Uncle Sam or state and local governments.
For a very rough example, if income was $120T and taxes were $10T of that, then Tax Freedom day would be
10/120 = 1/12 of the way through the year - January 30th.
It's worth noting that because of varying individual tax burdens, the country's Tax Freedom Day may nor not be an individual's Tax Freedom Day.
For further reading on this, check out the PDF available here.
Cost of Government Day
As best as I can tell from their methodology, this is calculated similarly to Tax Freedom Day, except the numerator is different. Instead of counting tax payments, it counts "Federal Spending + State Spending + Regulatory Costs". The first two are fairly straightforward, but the third bears further investigation.
According to this part of the report:
Our conservative estimate of total regulatory costs takes into account only the cost of complying with regulations: the material resources and labor needed to carry out compliance. For example, if a regulation requires new pollution control equipment power plants, compliance costs include the costs of manufacturing, installing, operating and maintaining equipment.
Thus, unlike the first two components, which are relatively easy to account for (governments release their budget figures), they're estimating the cost to all businesses to implement a given regulation. They base some of this number off a "Crain report" which they don't link to anywhere in their articles. With some persistent googling, I found this WSJ article where they announce the results of their study. However, they don't go into their methodology there, so I can't comment on it. According to the original site:
Crain uses a World Bank index that is more comprehensive than the OECD index. The index values come from 1,751 data points. Significant advantages over the OECD index include: 1) larger data series, 2) Regulatory Quality Index (RGI) covering international economic regulations in addition to domestic that newly includes rules and mandates affecting factor markets (for example, Americans with Disabilities Act), and 3) the World Bank index covers all business sectors.
Side note: The graph on that page is highly misleading. It shows a huge spike in days to meet the burden (~50 days -> ~70 days), but this is apparently due to a methodology change explained by the above quote. No attempt is made to recalculate previous data using the new methodology or to describe the relationship, so you can't draw any direct correlations between pre-2009 data and 2009-and-on data. This also plagues their overall summary data.
I'm not qualified to pass judgement on their numbers, and they don't provide enough information for me to research them. However, there's some criticism of the Crain report's methodology you can follow up on here, the biggest point of which appears to be that they don't factor in the benefits of regulation to balance out the costs. After all, if a corporation has to pay to install something to meet a new regulation, they're probably going to buy it and have it installed - which is money flowing to another company that wouldn't have gotten the business otherwise. I don't have any hard numbers on that, but it seems logical that the money doesn't suddenly disappear.
As to why they differ so much, you may as well ask why a quantity of kilograms and a quantity of kilometers differ so much - they're measuring two different things, which aren't directly comparable. They're using the same system of numbers, but there's no meaningful comparison.
Tax Freedom Day measures the income from all taxpayers to the government at all levels. This includes everything from income taxes to estate taxes, and corporate gains taxes to city wage taxes. In 2010, this figure was $4.7T (source), of which $2.2T of which was federal. The same year, the federal government budgeted $2.1T and spent $3.4T (source). The difference between the two numbers ($1.2T) becomes an increase in the federal debt. I don't have numbers for each state/local government, but it's on the same principles.
If that was all of what Cost of Government day measured, it would be an easy calculation. However, it's not. Instead, it attempts to measure how much money every company in the country had to spend to comply with regulations. However, unlike federal budget numbers, there's no hard data on this. Most companies don't reveal their books to that level of detail, and even if they did, it'd likely be rolled into "Operating Expenses", "Salaries", or something similar (no source) This is a burden on the company in addition to taxes (or possibly including taxes - since the methodology is unclear, I can't say for sure). But you can't track these payments and quantify them, because they include actions not taken as well as actions taken, money not made in addition to money spent, and so on. You can take the dollar value estimate and project that over the calendar year, the same as you can with tax revenue, but there's no relationship between the two sets of numbers at all. The government could suddenly double everyone's taxes without increasing spending, and TFD would move and CoGD wouldn't. Or vice versa.
All we can say for sure is that CoGD will be later in the year than TFD in every year the government runs a deficit (because the government spending portion of their number is larger than taxes), and CoGD may be earlier than TFD in a year the government has a surplus. But there's no way to correlate the actual dates.
- Tax Freedom Day is a straightforward calculation of
(tax/income * days/year) = days to pay tax
- Cost of Government Day is a calculation of
((federal spending + state spending + unsubstantiated numbers)/income * days/year) = days to pay for government.
- The two days have no relation as to when they fall, other than TFD is before CoGD.