The 4D classification is a gimmick that makes no logistical sense, the same as Giga and Strata coasters.
As Inverse pointed out, we can perceive 4 dimensions through real science in the world. So the fact that everything exists in time creates a 4th dimension, as we not only move physically, but through time as well.
HOWEVER, in coaster sense, the forth dimension is the ability for seats to rotate. A 5th dimension would mean the seats could rotate on both an x and y axis.
It is intriguing though, as thinking further, suspended roller coasters are 4th dimension coasters. Rather than rotating on a y axis like X2, they similar move on an x axis, swaying back and forth. This allows for 4 degrees of movement.