Rzeczywiście można się w tym pogubić.
Poniżej moje dywagacje na twój temat z pomocą pana Googla:

To GIVE UP means to stop trying to do something because you are not having success doing it:
(pol: odpuścić sobie, poddać się, zrezygnować, zaprzestać)
>> I still haven’t found a job, but I’m not giving up yet.
>> We spent all day looking for the dog, but we gave up when it got dark.
>> When nightfall came, we gave up looking for the lost dog.
>> I’ve given up trying to reason with you.

GIVE UP can also mean to stop doing something that you have been doing for a period of time.
(pol: zrezygnować, porzucić)
>> Her doctor advised her to give up smoking.
>> He gave up basketball in order to focus on his musical career.

To GIVE IN means to stop trying to fight or resist something:
(pol: ugiąć się, poddać się, ulec)
>> The factory workers have been on strike, but theyt don't show any signs of giving in to work out a compromise.
>> Arthritis has made it difficult for Walter to keep doing his job, but he won’t give in and retire.
>> Kids must try hard to resist giving in to peer pressure.
>> The authorities refused to give in to the hostage takers’ demands.