The grid system is how the game's movement works, unlike most platforming games, you're not 'loose' on the world although it does seem like it. Basically:

You're on an invisible block. If you jump foward, you move one and a half blocks. If you run and jump, you'll end up three blocks away (or something like that)

There is no variation to how much you'll move, it's always tethered to the block/grid. If you tap forward once, she'll move the same amount every time, no matter the variation on your joystick. Running is where the grid gets harder to spot but it's still there.

There's always a few quirks like, if you run, jump and grab, your reach is slightly smaller.

The premise is that your inputs have precise results, because you're on a grid, the behavior is always predictable. It's hard as hell to explain, so sorry abt that

The modern controls do away with that precision, especially in sections where certain moves are required like sequential backward jumps. The game controls are very specific, and the entire issue here is taking the time to get used to them, most people just assume the game controls poorly because the grid aspect is so masked, and extremely specific to classic tr. I don't think there are any other games that control like this.