[JakeGallagher]

We're in kind of a unique position as far as I can tell...
Our school considers us a team for everything that could hinder us, like when it comes to being on the team based on grades (usually not a problem, except near competition time when most of our seniors are in AP classes and start neglecting their homework for sleep after FIRST lets out), when we are going to competitions, the entire team has to go on a bus, so we have a really hard time getting our tools to and from the venue, and when ever we have to do anything that a "team" does for team unity, we're considered a team. That's because we're called a team.
As for anything else that "teams" at my school get, we're officially a club. Examples: school funding, being able to hang our banners in the gym, putting our trophies in the trophy case, and getting a second bus for the team's fans (all three of them, since the school openly disapproves of all FIRST related propaganda, but that's a totally different story) to go to the competition with us.
So to our school, when you ask if the FIRST team is really a team or a club, it depends on the context. If you're talking about getting anything from the school, we're a club, and we have to be self sufficient. If you mean when the school wants to limit us as much as possible, we're a team...and we're treated as such.
A pessimistic view of our situation, but a very real one.