There is a huge difference between how the Electoral College was designed to work, and how it works in practice. The intent was
that the immediate election [of the President] should be made by men most capable of
analyzing the qualities adapted to the station, and acting under
circumstances favorable to deliberation, and to a judicious
combination of all the reasons and inducements which were proper to
govern their choice. A small number of persons, selected by their
fellow-citizens from the general mass, will be most likely to possess
the information and discernment requisite to such complicated
investigations. (The Federalist Papers, Number 68)
That is, in those days when communication was slow and information-gathering was hard, it was not expected that the average citizen, or even the average state legislator, would know enough about the Presidential candidates and their platform to make an informed decision. So instead of voting for President directly, they'd vote for “electors” who would evaluate the candidates and do the actual voting for President. Electors were expected to be “faithful” only to their own consciences, and not to their state's citizenry.
But in practice, it took just a few years for the US to form national political parties and national Presidential campaigns. Electors would campaign on a “platform” of voting for a specific candidate (“I will vote for John Adams”), and people would get annoyed if the elector voted “wrong”, as with Samuel Miles in 1796, the first “faithless elector”.
Eventually, states gave official recognition to the idea of pledged electors who are a rubber stamp for their state's popular vote, and print ballots with the Presidential and Vice Presidential candidates listed as if voters elected them directly, with some fine print that a vote for a candidate is actually a vote for a slate of electors pledged to that candidate. And some states even passed laws penalizing electors for breaking their pledges, which were upheld in today's Supreme Court decision.
For example, in a blue state like New York, all 29 members of the Electoral College will vote Democrat. If any one of those 29 electors votes Republican, are those votes considered "Faithless Electors"?
Yes. Assuming that the elector was part of a statewide slate of electors pledged to the Democrat candidate.
For a swing state like Florida that's leaning red, do "Faithless Electors" exist?
It would just as possible as an any other state. Maybe Florida will vote Red, or maybe it will vote Blue. But either way, once the votes have been counted and a winner determined (even if it takes Supreme Court intervention, as in 2000), one of the two slates of electors will be appointed, and expected to vote for the candidate they pledged to vote for.