There are Thee ways to answer this question, I think:
History: In the past, Sociology was focused on the study of ‘Civilized Society’, whereas Anthropology focused on the study of ‘Savages’. Obviously, this is not the case anymore, which is why confusion happens, but this is part of the ‘reason’ there’s an observable difference in the first place.
Methods: Anthropology focuses more on Humanistic methodologies, most notably participant observation as a part of long-term fieldwork. It’s our thing. Most other methodological tools (interviews, discursive analysis, network analysis, etc) are shared, but participant observation…that’s ours. Along with a lot of the other crunchy postmodern stuff, like sensory ethnography.
Focus: Here’s the big one. Sociology has a kind of ‘Macro’ focus (and sometimes Mezzo, like, focused on family groups or something), always looking at people in aggregate. A discipline like psychology has a ‘Micro’ focus, looking at the individual. Anthropology (and, just as an aside, Social Work as well) have a Micro/Mezzo/Macro perspective. Anthropology situates the individual *within* the society, and shows how the two are related. This creates a lot of lovely tension; seeing someone as both a whole and complicated person AND as a product of and contributor to broader forces largely (completely?) outside their control.
Also, in North America, Anthropology includes Archaeology. And
that show Bones Physical Anthropology. And sometimes Linguistics.