The Commonwealth is an association of countries, some of which happen to have the same individual as head of state (not all). However for instance Canada has a

The Commonwealth is an association of countries, some of which happen to have the same individual as head of state (not all). However for instance Canada has a Queen of Canada who happens to have lots of othe "jobs" too. I think comparing that link to the Greenland situation is not viable. I think some of the largely self-governing territories are more comparable (Channel islands, Virgin Island etc).