It goes back to the colonies. In the British Empire the continental colonies were “the American colonies,” so British subjects from said colonies were called “Americans” for upwards of 200 years prior to the revolution. After the revolution, since Halifax was the only major continental port that remained in British hands, it made sense to call its colonists something else, while those to the south retained the name “Americans.”

Conversely, the Caribbean possessions were called “The West Indies” or “The West Indies Station.”