Hi there - a swivel is a forward turn (left or right) on the ball of one foot with the other (tracking) foot kept close. There should be a small amount of pressure on the inside of the ball of the tracking foot. The amount of turn is normally a quarter or less.
A pivot is a backward step turned to left or right. Most of the wight should be felt in the ball of the foot but the foot should be flat. The free leg should be held in front of the standing leg (as you turn). This is called Contrary Body Movement Position (CBMP). It's called this because it gives the effect of the body having turned. Please note that to achieve a correct pivot you shoul make sure that the stepping foot sshould be turned in and that slightly. It should also be a relatively short step. The body should also start to turn in the same direction. This doesn't happen with a swivel because the foot and body turn in the same direction.
Hope this helps.