Delay requires some waiting. You can postpone a meeting to a later date but that does not mean the meeting is waiting for something. For example: you have a meeting at first hour in the morning in you decide to postpone it to make sure everyone makes it on time. It does not mean you are waiting, as all members could be there on time.
Delay means there is some waiting. For instance, a plane is delayed because the weather conditions are not good. So there's a waiting until conditions are good for the take off.
Postponing can have a meaning of re-scheduling while delay is sort of waiting.