in the way i comprehend, a soul mate is soul that is here (friend/lover/family member/etc) who is meant to find and guide you some how. like a mentor. you meet and you hit it off, not necessarily love/romantic wise, and connect with one another.
however, the concept of a twin flame is singular. a soul mate is usually used in verbiage with the twin flame definition. twin flame is literally our other half. the concept that humans were joined at the back and zeus didn't want them to be more powerful than he. so he split us in two and we're now forced to wander and find our other half.
the twin flame concept is the basis of a song in hedwig and the angry inch
-- the origin of love
. all around great movie, imo.