Giving up is when you have a chance to change things, but you think it’s too difficult or not worth the trouble or just stop pursuing something and just give up on the spot.
Moving onis when you realize that you can’t change things or that it’s better that you don’t try any longer giving up or failure isn’t the best option. Moving on is another thing, moving on as in that you wouldn’t look back to the past and that you would be more successful than failure.