It's loosely used for the 73-77 4x4 F250s, but the term actually is meant to tell the difference between the 77 & 77.5 trucks. The latter of which has the negative arch leaf springs, making it sit around 4 inches lower.
It not being a factory term, it's all open to interpretation, but the folks who have a TRUE highboy (early 77 F250 4x4) are very particular about what is called a highboy. The term couldn't have existed until the 77.5 trucks came around, as everything beforehand was just a 4x4 F250. The bump-side (67-72) trucks have no involvement in the highboy/lowboy talk.
Highboy is used many times as a selling point for old 4x4 Fords. The same as the 351m becomes a Cleveland and the 360 is suddenly a 390 at selling time.