Yes, hard mousepads slide more on glass.

The smooth bottom of a hard mousepad has very little friction against a smooth glass surface. On textured wood, the wood’s grain and slight roughness grab the pad’s underside much better, keeping it in place.

If you’re using a glass desk, look for a mousepad with a rubber or silicone base. Or just accept that you’ll be nudging it back into position every few hours. Not the end of the world, but annoying if you’re precise about your setup.