Both were artists if using the term very loosely.
But one was Canadian and the other American.
Our Emily is a famous painter and writer. But mostly, famous for her painting.
Your Emily is a famous poet. Although she was born in the 1800’s she was born 50 or so years earlier than our Emily.
Yes, our Emily Carr is a Canadian:http://en.wikipedia.org/wiki/Emily_Carr
Yes, your Emily Dickenson is an American: http://en.wikipedia.org/wiki/Emily_Dickinson