Great question! While the core idea of every game is that they are simple run and jump games, they still have quite a bit of variety. Yes, there are games where you are simply expected to jump and that’s it. Take for example Bunny Run, where the only thing you need to do is time your jump correctly, the bunny actually automatically runs for you. On the other hand, there are games like Teleport Jumper. Teleport Jumper is still no doubt a run and jump game at its core. However, they have introduced the ability to teleport into the game, which adds another variable to the game to make it have some puzzle game elements.
Along with this, there are many different themed kinds of run and jump games to give them an extra flair. There are sports games like Basket and Ball, Christmas Games like 60 Second Santa Run, and even Quest Games like The Sun for the Vampire.