Hello Daniele. Good question, they are quite different and can’t be used interchangeably.
Give up- this is simply another way of saying ‘quit’. You would use this when you want to say you are abandoning something you were doing. For example, ‘I give up on learning to dance’, ‘I gave up eating meat for lent’, ‘I am giving up pursuing my dreams for her’.
Give in: This is like to stop trying to avoid something . The best example for this is to ‘give in’ to temptation. For example, ‘I had been eating healthy for a week but I finally gave in when I smelt the cake’.
The ‘give’ changes form depending on the tense you want to use. I hope this is helpful.