In game development, the terms Alpha and Beta are not applied concisely across all developers, that it probably should be is another argument entirely.
An Alpha build is supposed to be a game heavily in development, with systems, content, and other features incomplete. These very likely will change over the course of development and the final product will be different in most cases, particularly for more complex games.
A Beta build is a game that is deemed functionally complete and is now going through the process of refinement, this is not only bug fixing, but also fine tweaking of assets and systems, patching balance issues, and lots of other details that try to look at the game as a whole and see if the sum of it's parts works feasibly. Again, the chances of the product changing much in this time frame has a lot to do with complexity and the amount of effort gone into Beta Testing,
In some cases however you will find games where a Beta build is really closer to an Alpha build as it misses many key systems and/or game sections. There are also sometimes Alpha builds that are very stable, and considered closer to Beta status, but it's ultimately up to the dev to decide which designation the game gets.