Acadians are descendants of the French settlers of Nova Scotia in the early 17th century. They all stayed in that local area until they were forcibly ejected by the British in 1755. Then they scattered all over the place, but probably the largest numbers ended up in Quebec, New England, and Louisiana. Their descendants in Louisiana are now known as Cajuns.

French-Canadians, in genealogy, generally refers to descendants of the French who settled the Québec area, beginning in the early 17th century. They did not interact or intermarry very much with the Acadians, and so we have two entirely separate groups for genealogical research. Outside of genealogy, I guess any Canadian with a French name or who speaks French would be considered a French-Canadian.

There were Babin ancestors both in Québec and in Acadia. .