The difference is not about what happens at the border, at the PoE.
Your question is not so much about what is necessary to enter Canada, as it is about what is required to travel to Canada. These are very different things.
Prescribed Travel Documents are required to get aboard a flight to Canada.
In contrast, no matter what mode of transportation is used, once a PR reaches the PoE, the PR is entitled to enter Canada. The CoPR is not a Travel Document. But it is strong evidence of status, and in particular it has the PR's client number so the PoE can readily look up the traveler's Canadian immigration history and status in FOSS and GCMS. Thus, if the traveler has a passport properly establishing the traveler's identity, and a CoPR, that will ordinarily suffice to establish the traveler's identity and status as a Canadian PR.
Thus, the U.S. border difference is that people can travel to the border by private vehicle, or even walk across the border.
But obviously, if the traveler had lost PR status previously, a CoPR will not get the traveler into Canada as a PR: CBSA will see, in the system, that the individual no longer is a PR and accordingly deny entry as a PR.
Flying to Canada is different, because there are more strict rules limiting who the airlines may allow to board a flight to Canada. Only prescribed Travel Documents will get the traveler aboard the flight. A CoPR is of no help here. A CoPR does not get a PR abroad the flight to Canada.