In the context of public health, "compliance" is a word that is used to refer to the percentage of people who follow expert advice. The same word, "compliance", is used to describe how many people take their prescribed pills properly and on schedule. The word doesn't only apply for "mandates" or "orders", and as you correctly pointed out, what ultimately matters is what people do.
There were no orders but recommendations only in regards to vaccines. I understand you realize the difference between the order and recommendation. Recommendation does not require compliance.
And the burden was caused by lockdowns and complete absence of vaccines in Canada for a big while