Anthropology is the study of anything and everything related to mankind--prehistorically, via material culture (archaeology), language, social behavior, culture, biological development, etc. Anthropology has 4 fields: biological anthropology, cultural anthropology, linguistic anthropology, and archaeology. It's really only cultural anthropology that bears similaritie to sociology, as it tends to focus on the present day, and the study of groups of people. More often than not, the people studied are from a different culture than one's own, and will tend to represent a specific group of people who identify with each other as a group.
Sociology emphasizes social behavior, so has more of an emphasis on only the present. There is a tendency to focus on one's own society, but it doesn't have to be that way.
But the real difference is largely methodological. Cultural anthropologists tend to prefer qualitative methods (that is, asking questions, with long complex answers written in sentences). Sociologists much more often use quantitative methods (that is, statistical models and surveys that can be broken down into short sentences or words or categories).