States and Provinces are two very different things, and what most people don't realize is that Canada's Provinces should actually be called States. A state is capable of maintaining an independent government, should the need arise. A province does not have the governmental infrastructure to support the same.
To break it down more easily...
Provinces are still tied directly to the central government of the nation. They can be merged, removed, split apart, etc. by the central government without contest.
States abide by federal laws, but also have their own governments that, if isolated, would work in very much the same way as the central government. A state also cannot be subtracted from, abolished, or otherwise destroyed or changed by the central government alone.
Canadian provinces are an artifact of colonization. They've evolved over time to be much more akin to independent states.