Excellent question, hush4444!
This is not something I have ever thought of before from an American point of view but I can see why it may be an issue for (particularly Canadians) but many different nationalities and ethnic groups in North, Central and even South America.
From my side of the Atlantic, I can offer a similar situation. I am British but I am not English - I am Scottish. Although I am very much a Unionist, it does annoy me when people naturally assume Britain to mean England and me to be English, when in fact England is but one of the three component parts of Great Britain (along with Scotland and Wales) and one of the four component parts of the United Kingdom (Northern Ireland the subsequent addition).
I look forward with interest to more in-depth answers from your side of the pond! :)