The words rest, wrest sound the same but have different meanings and spellings. Why do rest, wrest sound the same even though they are completely different words?
The answer is simple: rest, wrest are homophones of the English language.
Cessation of work, exertion, or activity.
Peace, ease, or refreshment resulting from sleep or the cessation of an activity.
Sleep or quiet relaxation.
The repose of death: eternal rest.
To obtain by or as if by pulling with violent twisting movements: wrested the book out of his hands; wrested the islands from the settlers.
To usurp forcefully: wrested power from the monarchy.
To extract by or as if by force, twisting, or persistent effort; wring: wrest the meaning from an obscure poem.
To distort or twist the nature or meaning of: wrested the words out of context.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").