The general consensus,
pre alpha: is where you create the ideas, use story boards and concept art to come up with an idea before you start,
alpha: is the first working version of the game, something thats playable but not finished, this is generally when companies add major content and systems, bug fixes and other things can happen in this stage too, it all depends on the projects need. next is beta,
beta: normally has most major content in the game, though these systems can still change in beta, beta is normally for small tweaks, bugs, and optimizing the game for different hardware setups to run smoothly, some major things can change in beta, if they are problematic to a point where they cannot be delt with before release or a better idea emerges that wont take too long to implement, beta is generally much shorter than alpha, as obviously content and design take much longer than bugs, tweaks and optimization, but as mentioned above, this phase can be extended due to issues or major flaws, which would technically be an alpha revert, but most developers just keep the beta tag.
release: is obviously the final game.
this is a principle followed not only in game design, but in any software development that exists, hardware too actually does the same process.
many will say that its different from studio to studio, but it really isnt, they may call it something else, or they may do some little things here and there in different orders, but this process is usually followed pretty closely with most studios, as its the industry standard because its been found as the most efficient process to handle software(games)/hardware development.
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I believe each company is different, but the way i see it is like this:
Alpha - offers no online functionality (workshop is sort of inbetween)
Beta - offers some multiplayer features that require extra stabilization of online servers for latency testing
Demo - an incomplete version of a game with limitations for trial purposes (usually free)
ALL of these are meant for TESTING and BUG REPORTING before a final product is released
In the case of PC, the beta will most likely have almost 100% of the game completed but with minor behind the scenes technical fixes before the full launch and stabilization of the servers
online functionality has little to nothing to do with what is considered alpha or beta. well it can, but that entirely depends on the project, but, online functionality doesnt dictate what stage the game is in.
for instance, if you had software or a game, thats sole purpose is online features, you would want to start testing those systems in the alpha stage.