Strange fact: the Inuit are not classified as First Nations for some reason. Instead, they fall under the general rubric of "aboriginal". On the other hand, the Metis are regarded as First Nations, which makes little sense.
I think it would depend on who you asked for the Inuit. In places where they were both aboriginal and first nations those terms are mostly different articulations of the same thing, with personal preference of the person you are describing ultimately being the right choice.
This is a pretty good article on it through the lens of Australia.
