Retch: the act of vomiting, or trying to
Just the smell of the rancid meat made them all retch into the bushes.

Wretch: someone you pity for their miserable state OR someone you despise and consider lowly and/or despicable
He threw some coins to the poor wretch beside the pier.
Then the rotten wretch set the house on fire with me in it!

This definitely is not a pair of words to get wrong – imagine implying someone you pity induces vomiting! The way to remember which is which is to use w for who – who is the wretch? The verb retch is not a person and doesn’t have a w!