Thank you for the question.
They are two separate things. That's not 100% accurate.
However, we have a problem indeed if 10% of study permits granted are for Quebec, while Quebec makes up 25% of the population.
To apply federally for a study permit, you must first have a Quebec acceptance certificate, or CAQ. Therefore, you absolutely need Quebec government approval.
Because the Canadian government doesn't accept all applicants who have Quebec government approval, it means that more of them should probably be accepted.