When you are volleying, you must know if you are on the offense or on the defense. This will determine which kind of volley to use. For example, if you are near the net and you receive an easy floating ball, you are on the offense. Typically, a player will take a larger backswing on this volley, a larger follow through and keep their feet moving through this volley. They also should attack the closest opponent to them, to stop the ball from going to the deep player who has more time to hit a passing shot or throw up a lob.
However, if you are near the net and being attacked, or you are approaching the net to volley, but you receive a very low difficult volley, you are on the defensive. The word I like my students to think about in this defensive situation is "deflect." Minimize your backswing, try to stop the racket on impact and let the racket deflect the ball and try to be as still as possible. Try to return this defensive volley to the opponent that is farthest away from you. Think about your racket being a "backboard" when you are volleying in the defense. Remember, the backboard "deflects" the ball back when you strike it. Let your racket do the same thing.
Good luck on the courts!