Technically what EA put out for Battlefield: Bad Company was a demo, but there really isn't much difference between them. A demo contains a small portion of a game, usually put out to players can play them and decide whether or not they want to purchase the retail version of the game. Betas are much larger portions of the game, sometimes the complete game, put out to detect any flaws, bugs, or glitches. The public can then report these bugs and the game developers still have a chance to fix it, while in demos, the game is usually finished by the producing company.
EXACTLY.. lol
A Beta is released much sooner, so fixes can be made.. AND in this case it actually is going to be released much sooner than the full game, some of us just dont know it yet.