Answer
The main difference is the Domestic dog is part Order Carnivora, and the Canidae Family. The Prairie dog is not a dog at all; it is a Rodent belonging to the Order Rodentia.
The Prairie dog is a type of ground squirrel that lives in grasslands on the North American continent. They are named after where they live and the warning call which resembles a dog's bark.
Some of the differences between a Prairie Dog and Domestic Dog:
The Prairie dog is a herbivore, and a dog is an opportunistic carnivore.
One is a rodent, and the other is a canine.
Prairie dogs live in large colonies which can contain 15-26 family groups. The live in extensive burrows. The Domestic dog is often found within human homes.