Scores on a page, as you use the term above, are different from staves. Scores are groups of staves with parts performing within each score (so-used above) at the same time. Staves on the overall score for, say, a clarinetist are the separate staves performed one after the other.

What would be really helpful here would be a visual representation of the various ways in which a score can appear on a page. For example, a conductor's score, an individual musician's score, and a choral score that has a couple of scores (used here differently from the overall score) of several parts. These three types of scores, for instance, all look different from each other. Language sometimes fails where a visual representation would not. It reminds me of James Joyce's attempt to represent a fugue in Ulysses. Impossible, really. You can't show in words how a fugue really sounds--verbal fugue or not-- but Joyce was driven enough to try to do it--but you had to buy into his language. Word has it that he never again listened to Bach after studying the fugue master for the chapter in Ulysses--said something like Bach now bored him.