There is no such system that one is automatically enrolled in when registering a vehicle in either Canada or the USA.

In all the Canadian provinces, the only mandatory insurance coverage that a motorist is obliged to have is third party liability. In all provinces, it is possible to purchase additional insurance coverage for damage to your vehicle arising from an accident ("collision"), damage to your vehicle arising from non-collision causes ("comprehensive"), theft, and medical coverage for the vehicle operator ("accident benefits"). But these are all optional coverages.

These additional coverages (beyond the legal minimum of 3rd party liability) are not available to persons who are insuring a vehicle that is registered outside of Canada, for example, a person from Europe who ships their moto here to ride it around in Canada whilst on vacation.

Residents of some provinces will have coverage for medical services required as a result of a motor vehicle accident provided through their provincial health insurance scheme, but the coverage is limited to in-hospital services and visits to physicians. Coverage for additional medical services that might be needed as a result of a motor vehicle accident, such as ambulance, rehabilitation, home care, assistive devices, death & burial, etc. needs to be purchased from the vehicle insurance provider - this is the "accident benefits" coverage mentioned in the previous paragraph.

Non-residents who are visiting Canada as bona fide tourists need to obtain their own medical insurance coverage before arriving in Canada. This is entirely separate from vehicle insurance policies. Such policies are provided by private insurance companies, possibly companies that are not present in Canada, and one will need to very carefully examine the policy to determine what is and is not covered.

Michael