VATSIM is simply simulated ATC. There are people who work as ATC whom you contact while you are flying. I've never tried it as it looks very intimidating. You would need to know how to talk to ATC. You have to file flight plans and get your flight rule orders from ATC. I don't know if they have actual flight servers where you would see everyone else that is flying or not. You would hear everyone else that is flying.
I would like to try it, but it is too much just to try. I'm also 36 years old and am not into the teamspeak and communication thing so talking on my computer is a bit wierd to me. That's something that the younger crowd probably thinks of as second nature because they have always had communication with gaming.
I do believe you can mark yourself as an observer and join in to just listen. I think you would have to contact ATC and tell them your intentions so that they wouldn't have to worry about seeing you after contact. It all sounds really cool to me, but doesn't seem like it is for the casual flier like I am.
At WSPilots.com, we have done some casual ATC, but it was usually everyone flying the same route and not necessarily following true ATC rules. We usually only would have a handful of folks on the server. VATSIM is like actually flying IRL and talking to ATC as it is IRL.