The words retch, wretch sound the same but have different meanings and spellings. Why do retch, wretch sound the same even though they are completely different words?
The answer is simple: retch, wretch are homophones of the English language.
To try to vomit.
A miserable, unfortunate, or unhappy person.
A person regarded as base, mean, or despicable: "a stony adversary, an inhuman wretch” ( Shakespeare).
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.