Memorizing something means forcing yourself to remember it (for example, answers for a test, somebody's phone number, etc.). You can remember things both deliberately (as with memorization) or just naturally (for example, a pleasant childhood event).

Memorize: To learn something off by heart. Remember: bring to mind something or someone that happened in the past

Memorizing = spell some word several time so that you will not forget it. or keep something in mind. Remember = you recall some past event.