"Postponing" also means moving an event to a later date. For example, "The party has been postponed due to bad weather. It will be next Friday."

A "delay" means that it is taking longer than expected. For example, "I had to be at work at 8am, but there was a delay and I got to work at 9am." "Postponing" is a person doing something else, rather than doing what you are suppossed to do. For example, "I needed to do my homework, but I postponed it so that I could play games."