Other identifying terms:

Active/inactive couple or person, for certain dances when it is descriptive, or impractical to use numbers.   (Often 3 or 5 couple sets, 2+1 mixers, Virginia reel variants, squares, or Scottish dances)

Right hand / left hand (lady/gent) for squares

1st corner/2nd corner or right hand/left hand for contra corners (these are not necessarily neighbors, nor shadow/partner at set ends, nor are they precisely previous/current/next neighbors in a double progression)

Inside/outside for mixers or couple dances

Those who can, those who want, those who did/didn't

Leader (for lines)

Leads/Follows (squares, mostly)

Was top/bottom on the list?

Lone person/9 pin (mixers, odd number of dancer sets)

A/B for royal (double) squares

That's what springs to mind. 

Neal