History, the term "Indian" did apply to and include the Inuit, and is synonymous with the term "aboriginal peoples" according to the Supreme Court of Canada:
Daniels v. Canada (Indian Affairs and Northern Development), 2016 SCC 12 (CanLII), [2016] 1 SCR 99
Never, ever heard any Inuit refer to or even accept the term Indian or First Nations applied to themselves.