Sci, you are of course correct on the terminilogy. I also read the post you linked. Nice analysis of the situation, though I do not necessarily agree with all of your conclusions. However, it is clear that the Federation has become more unified and the central authority getting more power over the years (both real years and fiction years). This makes perfect sense to me.
Star Trek has always been focused on Starfleet, a federal institution, and we get much less information how things work outside of it. I'd assume there to be all sorts of political struggles going on between the member worlds that we never hear about. Even though UFP is has clearly more powerful federal institutions than EU, I still feel that EU is a better analogy for it than US. All these different worlds with different histories and applying for the membership reminds me of EU.
Also, it is true that the Federation Council seems to have a lot of power, but we know very little of how it is elected and how it operates. If for example it has appointed representatives from each member world and decisions that would introduce binding new laws on the member worlds would require unanimous vote, then in practice the Federation could not impose laws on its members against their will.