The term "Fox body" came from a directive that Lee Iacocca gave to the Ford engineering department in the early 70's. He wanted them to design a platform that could be used to build many cars (see Cenok's post above) and thereby greatly reduce the costs involved in manufacturing them. He told them to look at what Volkswagen was doing with the Fox. That platform was used to build the Fox, Rabbit (Golf), Dasher, Scirocco, 100LS and 5000. So Ford's internal designation for the project became the "Fox Platform", which has morphed into Fox body.
BTW, most everybody considers Fox body Mustangs to be 79 through 93. In 94 the Ford internal designation for the car became SN95 which ran through 98, then 99-04 are New Edge and 05+ are S197. You can nitpick all you want about shared parts, but the Ford designation changed in 94.