Choral Score
A score for vocalists that only contains the vocal lines. The instrumental parts are not there for reference. Generally, cheaper than a vocal score and requires multiple copies for purchase.
Facsimile of the Autograph
These are hardcover, research-quality reproductions of the original hand-written scores from the composer.
Hardcover
Some publishers print a hardbound, linen-covered version in addition to the standard paperback. The music inside is identical. These editions are beautiful though rarely cheap.
Orchestral Parts
Similar to a wind set, this is a collection of parts. In the case of strings, the numbers listed are the number of copies included, though generally these are available individually (often with minimum quantities required).
Paperback
When publishers offer multiple bindings (e.g. hardcover) or study scores, this is the "standard" version. If you're planning to play the music, this is probably what you want.
Performance / Playing Score
For chamber pieces, playing scores have all of the parts on one system. There are not separate parts for each player.
Score (Full Score)
For ensemble music, this indicates that the edition contains all parts on a single system (there are not separate parts for each player). In larger ensembles, this is for the conductor.