Give up means to stop trying or attempting something. It implies a sense of defeat or resignation.
Sacrificed means to give up something valuable for the sake of something else. It implies a sense of loss, but also a sense of dedication or commitment to a higher purpose.
Here's an example:
* Give up: "I gave up on my diet after a week." (Implies quitting due to difficulty)
* Sacrificed: "She sacrificed her career to raise her children." (Implies giving up something important for a greater good)
While both words involve relinquishing something, the motivations and implications are quite different.