I thought it was a crown corp too, but I don't think it is: https://www.canada.ca/en/treasury-board-secretariat/services...
If you look at their "about us" section, they just say they are "a corporation". https://www.payments.ca/about/who-we-are Although they were created by a law (Canada Payments Act) and have a public mandate:
Payments Canada has formed a critical part of Canada’s financial market infrastructure for over four decades. The Canadian Payments Association was created by the Canadian Payments Association Act in 1980, now known as the Canadian Payments Act (CP Act).
I think its because its a membership association (like a non profit), where crown corporations are structured like for profit companies where the crown (government) owns all the stock.