As already stated the game engine allows for fuzzy input. You can input a 270° motion as already stated OR you can input the bare minimum.
Inputing the 4 cardinal directions (up, down, left, right) in any order and composition (down + left can either count as down OR left, but never as both - this is why 270 is enough) will be accepted as a full circle motion.
Knowing this you can abuse it to your benefit. Have you ever seen Zangiefs going forward and backwards, which translates to left and right, very fast before a pile diver? They do this as footsies plus they buffer 2 of the 4 required cardinal directions, they only need to input down and up + punch to execute the move.
So good players actually input: back, forward, down, up + punch. It is really easy and fast once you do it a few times. This also works with the ultra, but the directions are not as arbitrary. You have to execute 1 full circle and then another one. During both full circles you have to hit the 4 cardinal directions in any order.
So left, right, down, up, down, up, left, right + all punch will translate into ultra, but left, left, right, right, up, up, down, down + all punch will just give you ex pile diver (one full circle + 2 punches)
You cannot abuse the ultra motion that good, this is why most players just execute 1 full circle and a 270 for the ultra, as it comes more natural.