The distinction matters because a lot of frustration is really aimed at the mill rate or the total levy, which are municipal budget decisions rather than something an individual appeal can change, while the assessed value, based on your property's recorded attributes, is the piece that can actually be corrected.
So the practical question is not when you can challenge the bill, since you cannot, but when you can challenge the assessment underneath it, and that window closes 30 days after your specific notice date, not a fixed date shared by every homeowner in the city.
If your assessment is accurate and the bill still feels high, the mill rate is a City budget matter, not an appeal matter. Get your hand-reviewed valuation from Joel Dyck.