As described in the patent, yes. You press one button, you start riding said mount. If it's glider mount, it automatically changes to the stag once you touch the ground OR to the fish if you fall to the water.

Palworld never had this "automatic change from one mount to another", at best it was the glider pals that you didn't have to manually summon in order to glide and went away once you touched the ground or water. I've skimmed the patent a few times, but I don't recall it having a case for going from creature-assisted-gliding to back on foot