Slimmer most often means “more slim” — thinner than before, or thinner than someone else. That is just slim with -er. In British English, though, a slimmer is also a person who is trying to get thinner by eating less and moving more. Magazines and clubs have long talked about “slimmers” in that way. American English usually does not use the noun like that; people say someone is on a diet or trying to lose weight. The verb behind the British noun is to slim: to make yourself thinner. You have to hear the sentence to know which slimmer you have: “a slimmer dress” (more slim) is not “a slimmer” (a person).