What would be an example of a non-native American?
A native American is any person born in America.
A Native American is a person descended from the original indigenous population of the Americas.
I'm a native American, having been born in the United States.
My friend Frank is a Native American, being an enrolled member of the Cherokee Nation.
Then how do you refer to people who were born in India?
So just to make sure we agree on the definition David,
Barack Obama is a native American. But Ted Cruz and John McCain are not.
Actually... I think the term you are looking for is "First Nations". If you use the term "Native Canadian", most Canadians will think you are referring to people who belong to the First Nations (i.e. the descendants of people living here before the Europeans took over).
I know this because there are Native Canadians
(i.e. what David refers to as "Indians") in my family.