One of the first exercise I propose on piano is fairly simple. Put your hand on the keys with your right thumb on the middle C and the rest of the fingers on the notes above, ending with the pinky on G. Then, one key at a time, go up and down the notes. You can go slow.
It seems a simple proposition, but I can assure you, if you’ve never tried it, controlling those digits is far from easy.
Some people do the “spider”. What it means is that instead of having a steady hand that stays close to the keys, they lift up all their other fingers when one of them is playing. The pinky and the ring finger would be high above the ivory when the index is pressing the key, for example. The goal is to use as little motion as possible, which will help conserve energy and get more speed.
Some people (it could be the same people as above), play more than one note at a time, meaning that after they press one key, they keep it down while pressing another. Both sound get mixed up. Now, sometimes that is what we want, but in this particular exercise, that is not. One note at a time is the desired effect. I call that “encroaching”
The opposite of the previous one is chopping the notes. That occurs when they actually do one note at a time, but they leave a big space between the notes. I ask that the notes be “legato”, sewn together if you will, next to each other, but not touching.
Some people drop their wrists, resulting in having the fingers resting flat on the piano. That has a simple name: flat finger. Normally, the hand should be in a position like holding a hot potato, the wrist should be aligned with the forearm. That one is not necessarily detrimental to the sound or the speed, but to the health of the player. Highly frowned upon.
Then, some people try it once, and then stop. I tell them to do it many, many time in order to get a smooth sound and a correct position. It can fill up a week’s practice. Paying attention to the details is what makes an artist.