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The general idea is that both are labels applied to them by colonizers and most people don’t mean either offensively. The best way to refer to them is generally with their tribal name if you know it.
A lot of authors, for example, specifically refer to themselves as such if you have interest in indigenous literature (I really liked Green Grass, Running Water if you want a recommendation)
Of course, everyone is different so you can always just ask.
Definitely agree on the tribal names, however in this case it seems like they want to apply it to the entire population regardless of tribe.
Canada would call them “First Nations” but I don’t know if there is an American equivalent.