Triggered by penwiper26's alpha vs beta plaint, though not a reaction to any of its actual content.
I write software for a living. The terms "alpha" and "beta" have particular meaning in that industry. I believe, though I'm not entirely sure, that the fanfic usage comes from the software release cycle usage. In the traditional release cycle, they mean:
alpha: most/all features in place, way buggy
beta: most bugs fixed, good enough to show to outsiders
Never mind that software never actually gets written that way. That's how the industry pretends it gets written. The terms give me hives because I cannot help but associate them with disastrous software projects experienced first-hand.
I suppose the fanfic usage means:
alpha: developmental editing phase
beta: copyediting phase
When I read the words "this is un-betaed", I know I can substitute the words "has spelling and grammar errors".
In both phases, the reader-of-fic is serving as an editor. I suppose the word "editor" isn't used because it's a real-world publishing role. The echoes of formality probably put off the fanfic writer. I wish it wouldn't. Editors are good things. A great editor can turn a decent writer into a wonderful writer. Use the word, assume the role, welcome the connotations. They're more suited for writing than the connotations of the software industry's term.
Like the illustrious penwiper, I am scared silly by the idea of reading somebody else's story in the developmental stages. I am only barely up to the task of shaping my own stories! Eek!
The real-world-of-paper writing concept I miss most in this virtual world of fanfic is the workshop. The small group of people who read each other's stories and pull them apart and put them back together. The trusted circle.
Okay, back to the struggle to the death with the current project. You should know that the story is winning at the moment. If my body is found slumped over my desk, you'll know what to blame.
 I put the punctuation outside the quotes because I am a crank.
 Think John W. Campbell telling Tom Godwin to make the stowaway a teenaged girl. Okay, that one's hokey, and he went nutso eventually. Think Moorcock, the editor who attempted to ruin an entire genre! Or more happily, think Anthony Boucher.