Yes, a score refers to sheet music that displays all instrumental/vocal parts of a piece of music. It is intended for use by a conductor, recording engineers, etc. to follow along with as the musicians play. It is different than the individual sheet music parts for each member of the performance group. I.e., the "full score" is different from the "Violin I" part.
And yes, in Hollywood jargon, score is often synonomous with the background music of a movie. The same terminology migrated to VGM usage. I use it myself in reviews and discussions, with the assumption that most people understand it as analogous to the actual soundtrack.
As for OST vs. OSV... there is no real difference. At one time OSV might have meant the music as it appears on the CD is exactly how it sounds in the game. But it's an outdated term.
Now, in this instance, yes, the "score" probably refers to the orchestrator/arranger. They might also be referred to as an engraver. Basically as Zanasea said, the person who produces the sheet music for musicians to play from and the conductor/sound staff to read from.
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