Does a withdrawn motion need to be recorded in the minutes? And what about a motion that was not seconded and was therefore not even considered?

Let's start with the latter. If your rules require that a motion be seconded before it is considered, the lack of a second means that the motion will not be considered. The Chair should say: "The motion is not seconded and will therefore not be considered. The next item of business is ___". Recording the motion in this case will make no sense, because it never had any status. Some people suggest that such a motion "died for lack of a second", when in fact the motion "never lived".

What about motions that are made and seconded, and are subsequently withdrawn? The answer depends on the progress made on the motion. There are times when recording the motion and the fact that it was withdrawn serves a useful purpose, and there are times when it doesn't.

For example, if a motion is made, seconded and opened for discussion, and shortly thereafter it becomes apparent to the group that the proposal is redundant (e.g.: the proponent of a motion to purchase furniture was not aware that there was a large inventory of furniture in the basement), there is no need to record the withdrawn motion in the minutes.

On the other hand, if there wasn't enough time to debate and vote on a motion and it was then postponed to the next meeting, and was subsequently withdrawn, the motion and the fact that it was withdrawn should be recorded in the minutes. If this is not done, readers of the meeting's agenda and the previous minutes will wonder where the motion disappeared.

It should be noted that, once a motion is opened for debate, the decision to withdraw it is made by the group, and not by the mover. It is technically incorrect to turn to the mover for permission to withdraw the motion, since the mover does not own the motion once it is opened for debate. For the bulk of the time, ownership is collective, not personal.