I'll give you my take, though if there is a reader out there who has a formal definition, please toss in your two cents.
Before the rise of subprime lending, we distinguished mortgage loans as saleable or not. That meant that the underwriting and documentation met the high standard of the agencies - FNMA, FHLMC or GNMA - and therefore could be sold either through securitization or as whole loans. Loans that did not meet these tough new standards remained in the portfolio of the lender. They might be sold but without the blessing of meeting agency guidelines, the attributes on the loans would be considered package by package, loan by loan.
When subprime style lending entered the secondary mortgage market, this paper was called, B, C, D paper. In other words, it wasn't as good as the paper that met agency guidelines, which would now be called A paper or prime.
Alt-A, in my view, implies that the paper is not quite prime, it is missing some key underwriting documentation - mostly likely verification of income.