I have no preference, so sometimes I will say Native American, sometimes its American Indian, sometimes its indigenous... No real preference other than I tend to use one or another based on context at times. Its more clear and not mildly politically loaded to say "Native American" in this context.
I do not really like using Indian to refer to Native Americans as I work with a lot of people from India. This is a personal preference, I don't correct people who say Indian to refer to Native Americans and I will often use it in a conversation where its already being used to avoid confusion or bad vibes.
An of course, there is the confusion you noted that can happen between the super-continent America and the country commonly called America.
Do USA schools teach that America is one continent divided in north, central and south America? Or is it America=USA ?
I'm from South America and we learn it's one continent
There are multiple, separate issues in the question.
As a matter of actual geological fact, North America and South America are separate continents (they have their own cratonic cores). Geographically they are considered distinct in the USA also. Central America is a cultural or political region refering to the isthmus -- it is not a continent in any sense.
Nationals of the USA are called "Americans" by USA nationals, and by people from other parts of the world, including Japan, Russia, etc (in their own phonologies). Canadians refer to USA nationals as Americans, and do not call themselves Americans.
Europeans frequently object to USA nationals calling themselves Americans, claiming that the word should refer people's of both North America and South America. People from South American nations seem to feel the same. Mexicans seem to me much more likely to refer to a USA national as "Americano" than they are "Estadounidense."
USA nationals will sometimes describe people from North and South American nations as be from "the Americas."
In my experience, a lot of people from the United States tend to conflate "America" and the "United States of America". It's a pet peeve of mine, so I sometimes correct them. But usually people just get annoyed with me. ;-)
This blows my mind, because it never occurred to me that this would actually be taught differently. But yes, afaik, in NA we're taught that North and South America are two separate continents. In Canada however, Americans are from the USA, but we don't generally refer to the USA as America. Only they do that. We refer to the middle nation in NA as The U.S.
It's hard to recall what I was taught about Central America, but I believe it was that it's sort of a region shared between both and only a colloquially separate entity.
So you learned "there are six continents"? That's really interesting. Growing up in the US, we always learned it as seven. I never really thought about that as something that was taught differently based on location.
(Unfortunately though, I think that ignorance is fairly common for a lot of aspects of life for people raised in the US.)
Side note: I was going to say "aspects of life for Americans", but realized Americans means more than just those in the US. So I propose a new term for "people from the US". USers. :)
At least from my experience, America is the US. If you want to refer to the giant landmass that makes up the majority of the land in the western hemisphere, you say "The Americas".
I do not really like using Indian to refer to Native Americans as I work with a lot of people from India. This is a personal preference, I don't correct people who say Indian to refer to Native Americans and I will often use it in a conversation where its already being used to avoid confusion or bad vibes.
An of course, there is the confusion you noted that can happen between the super-continent America and the country commonly called America.