No. Upper Canada (Ontario) and Lower Canada (Québec) rebelled in the mid-1830s, and the boys on the scene brutally pressed the uprising. The government in London panicked at the thought of a perpetually rebelling pair of provinces, so they created Canada West and Canada East (formerly Upper an Lower, respecively) and then joined them in a single province, with its own provincial parliament. They left the two entities to work out the details.
Canada West wanted les habitants
to provide public, secular schools for the English-speakers in Canada East (where the Catholic Church ran the schools), so they agreed to set up Catholic Schools in Canada West. So these are Catholic schools, and they are also public schools, in that the province pays for them.