Alpha and beta testing are nebulous terms that mean different things to different communities and different publishers. Here, they are really mashed into one category for the HG label and the process is broken up by the author/developer.
For the CoG label (outside of the contest) the process is different. The alpha stage is the per-production phase where you submit an outline, etc to the CoG team and they work with you on getting things green-lit. This continues all the way up through and includes copy-editing and an eventual “official” beta from CoG being presented to the community.