Not sure what you are talking about. There aren't a ton of scholarships in private schools for international students. Scholarships usually go to Canadian students. Public schools would be around 10K/year and private schools will be 25K and above. This is all without living costs.
The cost is not at all similar. There are pretty much no scholarships for international high school students at public schools and only a few for specialized private schools.
OP should expect to pay at least $13,000/year for public school tuition and significantly higher for private school.