This is similar to the argument over the language that the Irish folks speak. In common usage, it is called Gaelic. But there is a whole family of gaelic languages divided into two subdivisions. The only one properly called Gaelic in English is Scots Gaelic which derived from the dialect of the Irish language of Ulster, as I understand it. The proper term for the Irish language is Gaeilge. Translated into English (as it refers to the language) that would be "Irish". It is also sometimes referred to as Irish Gaelic. The English language as spoken by the Irish is called Hiberno-English. From that I think it reasonable to suggest that the various dialects of the language spoken in the US and Canada could be referred to properly as American-English, remembering that all the peoples of this part of the world live in the Americas.

All the best,

Mick