@juillet, you did pretty good describing the overall relationship between linguistics and anthropology, actually, but here’s a bit more detail:
Anthropology has (in the US) four traditional fields; one of these is linguistic anthropology, which deals with the interrelationship between language and culture—so you get stuff discussing, for example, the uses of ritual language in contexts like greetings, prayers, thanking, and so on.
There is also anthropological linguistics, which is variously treated as a part of linguistic anthropology or linguistics; it’s where you get things like discussions of directional systems embedded in the grammar of various cultural groups. In actual practice, this group gets lumped in with the linguistic anthropologists.
Sociolinguistics, which is very much a part of linguistics rather than anthropology—but see below—has (to make an overbroad generalization) two strands: micro and macro. The macro-level deals with things like language policy and planning, discourse structures and power relations, and the like; the micro-level deals with things like variation in phonetic or syntactic or whatever structures (e.g., you don’t pronounce things the same when you’re in a job interview and when you’re talking with your friends over pizza and beer). (There are other complications, of course—the macro-level is usually qualitative and the micro-level is usually quantitative, but not always. So it goes)
The complication: Sociolinguistics and linguistic anthropology and anthropological linguistics deal with a lot of the same fundamental issues, as @juillet said—therefore, it’s not uncommon for sociolinguists the end up in anthropology programs, or for linguistic anthropologists to end up in linguistics programs. This means there is a lot of cross-fertilization between the disciplines.