I understand what you mean now. The word "score" indeed has different definitions, depending on one's viewpoint.

The 'staff' is equated with each horizontal line of music, as it is usually short for a pianists "grand staff" (the coupling of a treble and a bass cleff).

I've heard 'score' used occasionally by people to generalize "the piece of paper that the music is written on". Specifically, a score is most often the aforementioned 'conductor's score' (or as I call it the 'composer's score') and it includes all of the parts. A 'chorus score' will occasionally include a grand staff with an orchestral reduction (so singers don't get lost ).

I just call it "line X, bar X", but only if we are reading the same piece of music (as most 'jazzers' do). The word system is used (again, if we are all reading the same piece of music) as a linear reference. Bar numbers eliminate all confusion here.

Some of my favorite music happens when everyone reads "the same piece of music".