How does British/French structuralism and functionalism differ from American Boasian anthropology?

British and French structuralism and functionalism are theories of human culture based on the idea that cultural artifacts and practices form a somewhat coherent structure that serves to provide society members with meaning in their lives and to preserve the culture itself. With this in mind, the anthropologist observes and records as much of the culture as possible with a view to fitting his or her observation into a coherent theory.
An example would be Malinowski's conclusions about the function of the Kula ring in the Trobriand Islands. This Pacific trade cycle is a formal cycle of exchanges of ceremonial objects. It seems impractical since the items exchanged have no intrinsic value, unlike trade items such as food or tools. Moreover the voyages between islands are long and hazardous, seemingly involving an effort out of proportion to the value of the exchanges. However, participation in the Kula ring is a vital means of establishing and maintaining status in one's tribe and alliances between groups. For a similar example from our own society one might consider that the value of an Oscar award is far less than the cost of producing a motion picture. But no one would remark "all that work for that little thing" upon learning that someone had won an Academy Award.
Boasian American anthropology is based on the theory of cultural relativism. Cultural relativism is a reaction to earlier theories of cultural evolution, which assumed that non-Western or non-literate peoples were primitive because their cultures failed to evolve into a modern industrial culture. Such theories sometimes included an assumption that the very thought processes of these peoples differed from those of "modern man." Hans Boas taught that each culture has its own history and value without being a stepping stone in progress toward a particular result. Boas studied the Kwakiutl of the North American northwest coast. He recorded everything he could, from details of religious ceremonies to recipes for berry pie.
Boas's students were taught to observe and collect information without any pre-conceived idea of what the practices of a given culture meant. Among his better known students were Alfred L. Kroeber, who was one of the founders of the anthropology department at the University of California; Margaret Mead, known for her studies in Samoa and New Guinea; and Ruth Benedict, who helped the US War Department understand the Japanese character in preparation for the occupation of Japan after WW II.
Boas's theories shaped American anthropology in its formative years. Part of the reason for the popularity of cultural relativism was that evolutionary theories had been associated with communism and Marxism. Cultural relativism seemed safely apolitical in contrast.