This is more a language question, and really doesn't have much to do with history in the way you have phrased the question. "Native American" (capital N) has a distinct meaning; "native American" (lowercase N) means something else. Context is key, here: if you're needlessly going around and saying "I'm a native American" without the "native" part being required or relevant in the conversation as a sort of gotcha thing, you are probably going to upset others.
No such thing as a native american, every one on this entire continent emigrated here. It's much more respectful , if you absolutely have to call them a name, to call them by their tribe. Like crows or Navajo.
I've even heard arguments that Columbus , who's Spanish wasn't all that great, wrote something close to "estos son un pueblo endios" . As in these are a people of god. India was known as Hindustan
Here read this I looked up the original name and found this, but I'm dead tired and I can't read it. I hope I wasn't too far off
This post has been removed as it's not a history question. Questions of terminology might be something for /r/Linguistics (their stickied Q&A thread) or possibly /r/AskSocialScience