Shooting off the dribble is a footwork skill wearing a shooting costume

The hands are the same hands; what changes is the quarter second where the body has to stop travelling sideways and start travelling up.

A player shoots forty percent from three standing still and twenty nine off the dribble. The instinctive diagnosis is that his shot breaks down under movement, so he goes to the gym and does more repetitions of the shot. Usually that is treating the wrong thing.

Catch and shoot gives you a gift. Somebody else passed the ball to a target, you were already facing the rim, and your feet had a full beat to set. The upper body does its normal job from a stable base.

Off the dribble the base is not stable, and it is the player's own responsibility to make it so. He is moving laterally or backwards, he has to gather the ball out of a dribble, convert horizontal momentum into vertical, and arrive at a release with his shoulders square and his balance neutral. All of that happens inside roughly a quarter of a second. Any residual sideways momentum has to be dealt with somewhere, and if the feet do not absorb it, the torso does, which is why the misses go left and right rather than short and long.

That last detail is a genuinely useful diagnostic. Short and long misses are usually rhythm and legs, meaning fatigue or force production. Left and right misses off the dribble are almost always the base. A shooter can film a session and sort his own misses into those two buckets in ten minutes and know more about his problem than an hour of generic form work would tell him.

Which is why the training that fixes it looks like footwork drills, not shooting drills. Stepbacks where the only thing scored is whether the feet landed simultaneously. Sidesteps into a hold, with no shot at all. Deceleration work in the weight room, because stopping a moving body requires eccentric strength and a weak player simply cannot arrive balanced no matter how good his technique is.

The players who make this look easy tend to be the ones with unusual lower body control, and coaches describe them as having a quick release, which is a description of the outcome rather than the cause.

Nobody has a quick release. Some people just get their feet down early.