The most common Opuntias in cultivation are arborescent (heavily branched trees), but there are 180+ species in the genus and they vary pretty widely. Your local prickly pear is probably different from ours. I don't know what a cactus pear is... presumably it's the same as a prickly pear. In Mexico, where these plants are an important source of food, the plant and the edible pad are called nopales, the edible fruit is called a tuna.
This plant was labeled O. streptacantha and there are plenty more in the back, to give some perspective about size.
This is our local Opuntia (native to the coast near here) which is more of a low shrub.
It's pretty common for people in Mexico, especially out of heavily populated areas, to plant Opuntias (typically O. ficus-indica) behind their house. Over the course of ensuing years, more than a decade maybe, the plant will grow bigger than the house. You can tell how long a place has been occupied by humans based on the size of the prickly pear out back, generally.