cxom says:
The Steam versions have seemed kind of glitchy though. If you launch stadium but then play Storm or Canyon Steam can't tell. Having two separate immersible platforms work together is going to require more than just Steam hosting the launcher.
Actually Steam gives you a message that the game has to be restarted. If you start Canyon and want to play Stadium, Steam closes the game and reopens it, this time saying "ingame : TrackMania² Stadium Open Beta". So it works, but it is a bit unefficiant.
And concerning the question about the key : Both keys from Steam and TrackMania.com work with each other. There should be no problem about that.