Yes a fajita is a burrito because the fajita uses the same wrap as the burrito does.
However the difference between a fajita and a burrito is in the meat used to make the fajita.
The fajita uses a different type of meat than a burrito uses.
Burritos are usually made with hamburger meat while a fajita uses mostly steak or ribs to make the fajita.
A fried burrito is called a Chimichanga.
A Chimichanga is basically a burrito that is made traditionally like you would any other burrito but instead of just being baked the burrito after it's made is put into a deep fryer and deep fried.
So when you order a Chimichanga you're ordering a deep fried burrito.
A deep fried burrito which is a Chimichanga is even more delicious than a regular burrito.
You can take those store bought packaged burritos and then deep fry those burritos and make homemade Chimichangas.
I do that myself.
I buy several of those packaged burritos and freeze them and then deep fry them or just heat them up when I need a quick food to make that will fill me up.