Hello!
So, a reminder helps you not to forget about something that you have to do. For example, you might have a reminder on your phone that you have to go to the dentist. It alerts you one day before, or a couple of hours before the meeting. This is individual. In case of reminders, you still have enough time to realise you have some commitments.
Prompt has to do with speed. You prompt someone in order to speed up the process. A prompt also serves an actor to think of the next line in his speech. See? Here you don't have 2 hours to say your next line. You have to be very brisk.
There you go! Hope I helped!