If we have an H-bridge made of 4 N-MOSFETs, the gate voltage applied to each pair must be different because in an active circuit the sources will have different voltages. How much?
This assumes an on-off type H-bridge and not a linear H-bridge used in bridge tied audio amplifiers.
If you ignore protection features (required to limit gate-source voltages when the supply exceeds the maximum gate-source voltage), to efficiently drive current through the load requires these gate voltages to be present: -
And clearly, the difference in voltage between the two driven gates for the MOSFETs that are activated is just the supply voltage.