Really, there isn't much of a difference. The term premier is merely an abbreviation of the French premier ministre ('first minister'), and in French they don't

Really, there isn't much of a difference. The term premier is merely an abbreviation of the French premier ministre ('first minister'), and in French they don't distinguish between the roles -- the Premier of Ontario is called le Premier ministre de l'Ontario in French, just like the Prime Minister of Canada is called le Premier ministre du Canada. In modern Canadian English it's conventional to use 'premier' to refer to provincial heads of government and 'prime minister' to refer to the federal head of government. This hasn't always been the case: until 1972, British Columbia referred to its provincial leader as its Prime Minister and before that other provinces did the same.