The words who's, whose sound the same but have different meanings and spellings. Why do who's, whose sound the same even though they are completely different words?
The answer is simple: who's, whose are homophones of the English language.
Contraction of who is.
Contraction of who has.
The possessive form of who.
The possessive form of which.
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").