Correct. That part of Canada used to be called Arcadia. So Cajuns didn't technically come from Canada, they came from Acadia. French explorer Giovanni da Verrazrano (same guy the Verrazarano-Narrows Bridge was named after) created a map where he named the entire east coast north of Virginia as "Arcadia," from the Greek term meaning "refuge" or idyllic place." Over the years various mapmakers gradually had Arcadia creep up the eastern seaboard, and then in the 1700s Champlain fixed it, with a missing "r" as in Acadia, to encompass Nova Scotia, New Brunswick, Prince Edward Island, and the Gaspe Peninsula of Quebec. It was 1710 when the British conquered French Acadia, and the Acadians refused to sign a loyalty to the French. The Treaty of Paris in 1763 ended the French and Indian Wars, and resulted in the unrestrained emigration of Acadians from Acadia (known as the Great Upheaval), although about 3000 were deported back to France. About half of those who were deported ended up being allowed to go to the French colonized, but Spanish owned territory of Louisiana, where most of the emigrants from Acadia had already gone. Acadians where living all over the eastern seaboard, and even in the Midwest. Slowly they mostly gravitated to Louisiana from all over the place in order to reunite families.
The term "Cajun" is a shortened, informal version of "Acadian." It started out as a pejorative, particularly when Cajun children, partly because of the Compulsory Education Act, forced them into formal schools and disallowed the Cajun French language to be spoken in schools. There are Louisiana Cajuns, and New Brunswick Cajuns, as well as Cajuns in Nova Scotia and the Maritimes, and New England. Generally, Acadians call themselves as Cajuns if they are from Louisiana and the surrounding areas, and refer to other Cajuns more formally as Acadians.
Louisiana Acadians are officially recognized as a distinct national ethnic group, same as people from France or Germany or anywhere else. That recognition has been extended to Acadians living in other parts of the country, as well. So call them Cajuns or Acadians, same thing.
Ever met an Acadian from South Dakota? They're up there. Not many.