How important is it to select the correct USPS shipping method?

USPS recently added a new ground advantage but I'm in Canada using a company that "re-ships" through USPS and the labels I print are in a partnership with USPS and that company and print with different service names that USPS uses even though they are the same USPS services.

One service ends up showing on the tracking page as "Parcel Select Lightweight" which I don't see in the options Amazon gives, the closest I see is "USPS Parcel Select", is that what I should choose when tracking shows "Parcel Select Lightweight"?

Also how important is it to select the correct service type, can it cause problems if I don't select the exact right service?