I feel that they have such similar meanings, but postpone for example in context of an event means putting it on hold for another set date ("We have postponed the wedding until next year")
Delay normally means that it will take place but at a later time ("The flight has been delayed")
This is a hard question
If you enter both words in the dictionary look-up ("delay postpone") you will not see a definition, but you will see a list of previous threads whose titles contain those two words. It's a very quick and easy way to find existing threads on a word comparison.
This thread is now closed. If you read the existing threads and still have a question, feel free to tack your question onto the end of an existing thread.