I've always used "BSC" when using an abbreviation for "British" threading...never used "BSA" except when referring to a bicycle or motorcycle of that specific brand (Birmingham Small Arms).
I know that there's a connection between the threading that BSA used on their machines and the BSC threading that was adopted as the British Industrial Standard, but I'm not going to stir the already-muddy waters by using terms that may make sense to someone who's studied British bicycle history, but only confuse everybody else.