The aeronautical experience requirements for various RATINGS are listed in 61.129, there is no instructor RATING. The ratings they refer to in 61.181 is when you want to say add on a helicopter RATING to your Commercial Pilot/CFI CERTIFICATE. In the FAA world, RATING sets forth the special conditions, privileges, or limitations on a CERTIFICATE. The Commercial Pilot/CFI are the CERTIFICATES, RATING is the privileges/limitations on the CERTIFICATE, e.g. airplane, helicopter, multi-engine etc.
In FAA world they are instructor CERTIFICATES, not ratings.
Rating, certificate, endorsement, licence, license, approval, authorisation …who gives a toss what you call it, or how you spell it, all that matters is what it allows you to do.