What's the difference between exaggeration and hyperbole?

Exaggeration simply means going over the top. An example is when you are waiting for your friend, and you've been waiting 5 minutes, but you say to him: 'I've been waiting for like half an hour!'

Hyperbole means UNREALISTIC exaggeration. That's the keyword. 'I've been waiting 5 years for you, where've you been???'

'This tree is as tall as a church' might simply be exaggeration, but that other tree being as tall as the moon, is definitely UNREALISTIC enough to be called hyperbole!