[Callers] "improper"

A question about terminology (maybe two). Does the term "improper" mean a formation, or a position? In other words, does that term mean a line of dancers that alternates gent/ lady/gent/lady down the right line and lady/gent/lady/gent down the left line, or does it mean gent in the right line, lady in the left line (all left/right designations based on facing the top of the set)? What makes it two questions is whether there's a difference in how you, as a caller, think about it, and how you think your dancers think about it. What I really want to know is whether there's regional variation, and whether it's different in English country dance and contra. And maybe whether it's changed over time. Here in Boston, I'd say dancers think of it as a formation, and there seems to be variation in how callers think of it (e.g., some callers will say "end improper" to mean gent/right, lady/left whatever position you're in—it comes up more often in English country dance than contra, but sometimes in contra too).