I agree that the current wording might be a bit confusing and inappropriate.
movie-rating should indeed become content-rating to better apply to the domain of TV shows. I would however prefer singular to plural here, on the one hand to further distinguish it from the other kind of rating (for which the plural term "ratings" established itself as a common name) and because it better highlights the process of rating something and not the fact that it is a multitude of ratings that's the outcome, as it is with the other kind of "audience ratings".
Turning television-ratings into viewer-ratings might not be as urgent, but I might agree that it further helps to differentiate it from content rating and clarify its meaning. That tag actually once was nielsen-ratings, but while this was quite explanatory and clear for those who know it, it was far too specific and localized for an international site. So I turned it into the broader television-ratings which I agree might not be as clear as viewer-ratings. (Afterall, viewer-ratings seems to be a special sub-tag of reception anyway, but I think it's worth its own tag, seeing how broad reception is in the first place.)
One could even go a step further and call it something like audience-measurement to better distinguish it from content rating, but I don't think that would help the explanation, since it seems a bit too abstract and afterall the word "ratings" has established itself as accepted terminology for a TV-show's performance. Or maybe we could use audience-measurement and make viewer-ratings a synonym of it.