First Nations is what they say on the CBC, but "Indian" hasn't been stamped out completely.
Well, the same is the case with Europeans, Asians, and so on, so?
We have smaller identities, and larger group identities, it's not belonging or being categorized in one precludes the smaller more unique identity...
Does "Inuit" have two meanings?
Part of it is the word Eskimo. Not popular and falling out of fashion, people look for a replacement, and grabbed what a large subgroup of the people called that calls itself. And thus mislabeling those that are not in that subgroup.
To stretch the analogy again, lets assume for some reason "North American" has become a word to avoid, so lets just call all North Americans what the people from the USA call themselves to be more considerate. And the Canadians aren't happy with that.
I'll admit "inuit" is pretty widely accepted nowadays, but it's not universally so. The relevant ANLC page gives a good summary of the situation: https://www.uaf.edu/anlc/resources/inuit_or_eskimo.php
I've heard plenty Indians call themselves Indian. Probably tied to locality
When my father was in school in Northern Ontario they were having students cross out "savages" in text books & write in "Indians". While I was growing up the term was moving to aboriginal