I'm sure people could correct me on my use of terms, but here's how I'm defining them for my own purposes:
Alpha: Putting in core systems and testing them and seeing base functionality. No GMing pretty much at all or story movement, so it's effectively a sandbox, with just some light seeding of story elements as a prologue. I was not expecting us to be this busy at this point in the game, and I absolutely do not blame anyone if they are like, 'I can't find things to do or feel it's difficult to get involved or code is too hard to use and offputting'. Those are all extremely fair criticisms and a lot of those things just aren't ones I'm focusing on right now, since there's too many core aspects I'm working on that I think would help long term sustainability. Also a fair criticism to say I should expedite things to help people have easier access now when they are hyped, but I see it as a trade off. It is very reasonable for a lot of people to not be interested in the game in this state, which is where we are right now.
Beta: When it's no longer a sandbox, and we're actively GMing and moving the story forward, and see how a lot of the macro systems work in progress. I view it as entirely possible I could have made a catastrophic mistake or two that will make revamps necessary as I see how things come together, which is why I'd prefer to call it a beta in the full knowledge I might have to wildly tweak systems, and this is where we hope to really put in most of the systems that would help players create their own story long term. Dynamic rooms, storytelling support for PRPs, and similar systems.
Release: Probably will aim for when the first major chapter of the opening story is done, to coincide with me being satisfied that no major system will need to be completely overturned or there will be a need for mass retcons and things like that. Where I picture a reasonably consistent continuity and if I dropped dead of a heart attack the game wouldn't immediately lapse into stasis even if the metaplot stalled.