I think the whole Alpha/Beta nomenclature is effectively obsolete and a holdover from earlier water-fall methodology. I completely fails to reflect a number of important changes and milestones in development and results in an absurd 2 and a half years of Pre-Alpha in which import changes are ignored.
Based on my experience in the industry I would propose a new pattern that reflects the way games are actually made now a days, their are 4 stages, experimental, prototype, production and refinement.
Experimental stage - Characterized by tiny team size, typically 1 designer and 1 artist. The designer is typically modding an existing game at this point and doing massive brain-storming of the highest level goals, the artist is producing 'throw-away' art to accompany the designers modding as well as concept art to establish the overall artistic tone. The whole game concept can be rejected/abandoned by its team. The publisher has not made any real financial commitment to the project and the studio may still be trying to 'sell' the idea to the publisher. Publishers may ask that experimental squeal projects be started immediately after a title proves successful. Experimental stage products are ALWAYS secret and rarely ever leak because they are so small.
Prototype stage - The key change is some kind of initial green light from a publisher to invest more resources in the project. The team is given a producer at this point as well as full time programmers and more concept artists. Work now begins on a new engine if its needed or a search is made to license an existing engine and bring in talent familiar with the licensed engine. The original artist might be put under a more senior artist and the new artists make the bulk of the projects concept art during this stage as well as the initial artwork for the new engine if the formats not compatible. The designer continues working with their old-engine mod and gradually transitions to working on the new engine, a programmer dose the heavy lifting to build the new engine and port over all the work from the prototype (probably re-writing every line of code the designer wrote in the process). This stage ends when the publisher give the critical green light for full production. An expansion pack could be though of as completely skipping this stage. Projects are rarely if ever announced at this stage because the publisher hasn't fully committed too it and it may still cancel it.
Production stage - The now much firmer commitment of the publisher is backed up by their spending the bulk of their financial commitment for the project. Team size grows rapidly now and reaches its peak. Artwork shifts to final production, concept artwork begins to drop off and a transition to final artwork begins, this requires a much higher number of artists and artist may swell to more then half the team at this point. This is the final point to add core programmers to the project, the Prototype programmer would almost always become the lead programmer if they weren't already. Junior designers might be added now if applicable. The game design still has some fluidity but its only in the smaller details of design and get increasingly smaller and smaller as design progressively narrows down, the exact speed of this narrowing varies from studio to studio and designer to designer. Firaxis takes a very fluid approach from what I can tell, features remain very much 'up in the air' during most of production. Alpha and Beta occur some ware in here but as has been noted their very mushy concepts now, some ware along the way testers are added both internal and external 'fan' testers, generally no publisher testing is happening yet. The programming team will mostly be implementing core features at this stage, they will need to get some kind of AI running though it will be sucktastic for a long time, they debug generally only the most severe stuff like Crashes. A title is typically first publicly announced late in this stage after it becomes clear the project has good momentum and isn't going to implode or fizzle.
Refinement stage - Defined by the locking down of the games design. From this point on the only changes allowed to the code are bug fixes and the infamous 'crunch time' may set in if debugging is slower then expected, because it is fundamentally impossible to add programmers this late and a deadline is fast approaching the only way to debug is for the programming team to put in extra hours. Their is little or no change for the art department though, they would continue to churn out final game artwork which can be added up to the last moment. Some studios plan for all artwork to be completed prior to this stage and artists would now be re-assigned to other projects. The publisher begins doing testing at this point and begins planning a marketing strategy which can be another large financial commitment by the publisher. The publishers assessment of the titles potential will determine how much they go with minimal marketing or are really willing to 'double down' and spend for a marketing effort costing more then the whole development cycle up to this point. The design team will now be focuses entirely on balance and improvements that can be made by adjusting data rather then code. Near the end of this stage comes a publisher certification process in which the publishers testers verify that game meets minimum levels of playability and stability, the publisher is verifying that the bugs their testers found earlier have been fixed. Financial rewards/penalties for making/missing these 'certs' may be involved. The stage obviously ends when the project goes gold following a successful certification, though it's not uncommon for some more work to be done after gold resulting in a 'first-day-patch' that available before the first boxes leave the shelves.