Technically, as has been explained to me, an autograph manuscript musically speaking is not (definitionally; it could be, just not by definition) a work with the composer's name on it- even copies by other people will often say "by ... such-and-so". An "autograph" is in the composer's own hand (and since we often don't know a rare Renaissance or Baroque composer- or a rarer Classical composer's - signature - telltale signs of autograph-ness might include loads of crossed-out bars and even pages, and other things that shout "this is not a fair copy made at leisure by someone else, this is someone's working manuscript!" -- or else if it was someone else's copy, either it was for their own use and such mistakes were ... ok, or with all those copying mistakes and extra pages needed, the library that hired them should have fired them quickly. (Almost definitely autograph ms include, say, the score of Ferdinand Hiller's symphony in F minor of 1832.
and lots of other messy examples.)A holograph, is an autograph that, furthermore, the composer has signed.
An abschrift is, I gather, a copy in manuscript- not necessarily of a manuscript (sometimes it's a copy of a score!)- all one can say is that it's a "manuscript copy", that is, a copy in manuscript. (This phrase can be misleading; there are some abschrift that are handwritten- manuscript, that is - copies, often made by people for their own use and study, of works that they found in libraries in published score, for example. But they aren't direct copies of the original ms, or even of copies of the original ms. Still, any "handwritten copy" of a work is, I gather, called an ms. copy. It's not exactly easy to tell- unless the work never was published in typeset, commercially distributed score- what kind of score it was a copy of. Just saying.
(Abschrift is the German term for it, which you'll run across often if you use the very, very helpful RISM Online - which allow me to recommend most strongly.)