First, understand that there isn't really a Canadian federal health care system. The Canadian government (federal) transfers funds to the provinces, which operate health plans for provincial residents. The provincial health plans control the number of available specialists. A health care provider can only bill the provincial plan if they have a billing number, and the provincial plans manage billing numbers to limit/encourage specialists and to make sure doctors provide services in less populous areas. I don't know if it's still the case, but historically there was no private alternative available (so doctors couldn't operate a private practice that didn't need a billing number from the provincial plan). If provinces chose to allow private practices, the federal government threatened to withhold funds from the plan.

As with most western democracies, Canadian doctors are well compensated in comparison to the rest of society. But it is generally understood that they can make more money in the US if they qualify for immigration (and many can because of rules allowing people with specialist skills to get immigrant visas). This also contributes to reduced supply of specialists, and longer waiting times.

To get to see one of the available specialists in Canada, you have to have a referral from a primary care provider. Here in the US (in my experience) a referral is as simple as saying to your GP, "I want to see a cardiologist." Then your GP says "Oh, sure, this one's very good. I'll refer you." In Canada, your GP has to follow plan guidelines for referrals, and confirm that it is warranted. Then you get on the waiting list for the specialist. You'll wait for a consultation. At the consultation the specialist will determine whether or not you need treatment, and the urgency. Then you go on the waiting list for treatment.

Of course, Canadians with the financial resources are free to travel to other countries to obtain medical treatment more quickly. The provincial medical plans do not pay for treatments obtained outside of Canada. Medical "tourism" is not that unusual, including travel to the US and other countries.