In 1867, Canada became a federation of provinces of the British
Empire. These provinces, and indeed the Dominion as a whole, were
not states; they were still completely subject to the executive,
legislative, and judicial dominance of the Empire. Further, the
intent in 1867, which after all was only a couple of years after
the American Civil War, was for Canada to be a far more centralized
federation than the United States, so the symbolism of calling its
components "states" would not have been desired.
While Canada and its provinces have since gained independence, and thus statehood, and the provinces have developed broader jurisdictions than had originally been intended as a result of a series of court rulings, there has never been any move towards referring to Canadian provinces as "states". This is mostly due to Canadians being accustomed to using the term "province", but perhaps it is also partially because Canadians see having provinces instead of states as a way to distinguish themselves from Americans.
Contrast this with the United States, where the colonies originally formed a confederation under the premise of being (or seeking to become) independent states, and Australia, which was intentionally taking cues from the US,furtherevidenced in the fact that it has a House of Representatives rather than a House of Commons.