Just as an addendum to Rolling Circle's appropriate comments :
i) There was in fact,in the seventies, a Commercial Flying Instructors Rating! Would you believe "Commercial" was typed above the ordinary F.I. title on your Rating page!
ii) To be a "Commercial" Flight Instructor these days means being employed by a CAP509- Approved FTO and,after appropriate extra training in house, being subjected to examination by a CAA appointed Examiner.
This allows you to instruct with that FTO only and is invalidated as soon you leave.
I think that's the case anyway - always open to further comment?
Rgds, Sleeve.