The words reek, wreak sound the same but have different meanings and spellings. Why do reek, wreak sound the same even though they are completely different words?
The answer is simple: reek, wreak are homophones of the English language.
To smoke, steam, or fume.
To be pervaded by something unpleasant: "This document ... reeks of self-pity and self-deception” ( Christopher Hitchens).
To give off or become permeated with a strong unpleasant odor: "Grandma, who reeks of face powder and lilac water” ( Garrison Keillor).
To emit or exude (smoke, for example).
To inflict (vengeance or punishment) upon a person.
To express or gratify (anger, malevolence, or resentment); vent.
To bring about; cause: wreak havoc.
Archaic To take vengeance for; avenge.
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.