Well, another clue ...if it helps. I did receive both of these from different gardeners in different parts of the country. So they aren't native to here, they came from elsewhere.
Opuntias are not easy to identify. The Flora of North America will give you a technical intro to what's native to the US and Canada (yes, prickly pears make it into Alberta and Saskatchewan!) http://www.efloras.org/florataxon.aspx?flora_id=1&taxon_id=123045
Also, perhaps add photographs of the entire plant? Or are the pads similar in size and shape on both?
Here are two pictures. Actually the pads are smaller on one than the other. Not sure if that helps at all.
The first picture is the one with the yellow and red blooms. Second picture would be solid yellow blooms and bigger pads.