I guess that someday (or it already has) the alpha release will replace what used to be beta (a limited release for a select few testers).
Uh, an alpha release used to be even less
finished than a beta. The beta was the final stage before release, until someone bright came up with the idea of calling something a gamma release (sheesh). Fortunately, the term "gamma release" hasn't survived, but both alpha and beta are used as I describe it, which is exactly the opposite of how you seem to describe it.
I always thought that once you release something to the general public it's not really a beta anymore.
Here's a pretty great quote about what makes an alpha or a beta release:
Alpha: Something works.
Beta: Something works well.
Whether the software is actually made accessible to the public or not doesn't come into it, there's a long and great tradition that beta, alpha and even pre-alpha software is available.
My guess is that the words "alpha release" and "beta release" were originally meant indicate that they're actual "releases", that is "packaged for the public to try out if they dare", while whatever comes before isn't
releases as such. Today, this kind of separation is essentially meaningless for many software products, which are available almost straight out of CVS or other versioning systems.