You have to match into the first year, whether that be transitional or whatever, so you can choose as much as you can choose where you match. I'm pretty sure you do both matches at once but not 100% sure. Most people I've known have gone to different places for the internship/transitional/whatever year and their chosen residency, but for sure some stay in one location.
A transitional year includes exposure to all sorts of things, what
LizzyM was talking about. Some things you have a choice; like for anesthesiology, for example, you can choose to do either a transitional year or a preliminary surgery year before starting the anesthesiology residency. I'm not sure what the rules are for things like radiology.
Like erin682 said, almost all EM programs are 3 years, and some are 4. There's tons of info on the EM forum about debates over whether one is better than the other.
You can check FRIEDA for all residency information (if you're a dork like me) to see what sorts of things are available for different specialties. Also, if you're really curious, spend some time reading the residency forums, particularly their FAQs. There's some great info there for the curious.
edit: I remember at some point in the past I heard that the term "intern" was going out of fashion. Can anybody in the know comment on whether that is the case or not? I suppose this is more specifically for the straight 3 year residencies.