I thought I might as well clarify how to simply distinguish Alpha from Beta development stages.
Alpha: major, planned features are still to be implemented. Focus is definitely not on tweaking, bug fixing, balancing, polishing or UI, although work in these areas can obviously happen if need be.
The game, both in gameplay and codebase, can easily undergo very radical changes multiple times during this stage. This is definitely where DF is at.
Beta: all planned major features all already implemented. Planned minor features might still be missing, but all core systems are pretty much set in stone at this point, only requiring more fine-tuning at worst. Focus is heavy on bug fixing, balancing the game systems, usability testing, core testing, big emphasis on polishing the game up for release, etc. This is where DF will never get to
I'll also note this distinction rapidly losing meaningfulness under current game-dev standards. Agile development and iterative approaches are the norm today, and games typically undergo several implement-stuff-then-test-and-polish-things-up cycles right from the very first stages in the process.
The whole Alpha/Beta distinction is mainly an heritage of the holder approach which is common in other engineering fields, where you usually do all the big-ass design work first, then go implement stuff and changing things as you go is not really a viable option.
This is also why the standard for numbering in-development versions of a game with the build number is way more common today then the more traditional xx.yy.zz one, although you'll still see a sub-version digit appended to the build number to track bug-fixes and the like.
It's funny because the an increasing number of developers are using Alpha/Beta labels to name their products for marketing reasons.
I.e. you'll come across 'Alpha' version of games which look a whole lot like finished products which only lack content, but are otherwise pretty much complete, implementation-wise (people love getting access to in-development builds and will gladly pay good money for it, usually in the form of a pre-order).
While other times games are labeled as 'Beta', but it's immediately obvious tons of work still needs to be done and the game would likely turn in a completely different beast in due time (this especially seen in browser-based, free to play, pay to win games, as people don't really like spending money on virtual goods if they feel like the game is not mature enough).
When developers these days talk in-development games which are not going to be publicly available, they usually refer to the playable form as 'internal build', 'experimental version' or something along those lines instead.