I'm a native speaker of English and I was unaware there was any difference in pronunciation between these two words. Unless you mean the difference is between those two and 'pick'?
there is a very subtle difference..it might also depend on your regional accent..."peek" is pronounced with a slight stretching of the 'e' sound, ie pe..ek, where as "peak" is pronounced without...
As another native speaker, no, there is no difference.
"peek" and "peak" are both pronounced identically \ˈpēk\
They are homophones.
Pick is pronounced \ˈpik\.
Piece and peace are also homophones and pronounced identically \ˈpēs\ while piss is pronounced \'pis\.
Apparently you have trouble distinguishing between ē and i sounds but there are only two different sounds in those word triplets, not three.
I'm a native speaker of English and I was unaware there was any difference in pronunciation between these two words. Unless you mean the difference is between those two and 'pick'?