It depends on the province, but generally speaking, everyone has access to free healthcare across canada. Quebec is vastly superior in what they cover due to additional policies on top of what canada suggest/covers.
I have private insurance on top of that, so my situation is different.
My insurance work like this : They have no right to contest what i am being prescribed by my MD, be it medication or tests. They have categories that are covered by x %. For meds, its usually 100% for any generic and 70% for originals. No question asked, no co pay, and unlimited funds (no maximum ceiling). So even if im on a very expensive med, and even if its not approved for my condition, they will not contest it. My insurance company DO NOT have access to my medical records.
For tests, its usually free with our public healthcare. But if i want to have the test done faster, i can pay out of pocket and they reimburse 75% (with my private insurance), no matter what kind of test is required. An MRI, for example, is around 600$ CAN when going private (1 week wait time for scheduling + results). My insurance pays 75%, so i end up paying 150$. Very reasonable.
Now, its not all bells and whistles. Wait time in any emergency room on a normal day is 10-20 hours if you're not dying (read : if you dont piss blood you're fine, just wait). Public testing, for example, have enormus waiting times. MRI have wait times of 3 months up to 2 years depending on your region.
I pay 40% of my income in taxes, on top of having the highest sale taxes of any province in canada.
So its give and take. Nothing is free. I still prefer my system to what you guys have in the states.