Gosh, its quite hard to discuss this across several days with several people. I'm going to create this answer and encourage people to comment and edit to arrive at collections of synonymous tags. Suggested lead tag shown first:
Please add or remove or re-group these - but please add comments as you do so, so people can see your argument and return them if there is disagreement. I've started with a suggestion, but honestly I'm not that enamored of movie-rating.
Meaning: classification or certification of a movie by some national or regional body, e.g. MPAA, BBFC, CBFC:
content-rating: age-rating, classification, certification
Meaning: a system of reviewing the quality of a movie through numeric score, stars or similar:
movie-rating: star-review, rating, review-system