Just a small pet hate here. These terms keep flying about and it be good to get this cleared up. This is just response to many 'Beta' releases which aren't even near Alpha.
Alpha: Core engine is functionally complete. Very few major changes to the engine will be made beyond this point. All gameplay logic is about 70% complete with assets to match.
Beta: Core engine is complete. Gameply logic is complete with assets to match. Game should not have any tech hangs or crashes/ Anything from this point will be bug fixes.
Final: Shippable. This is the version that is played by the public. This should not contain any noticable bugs. The exceptions can be minor graphical glitches, minor sound glitches.