The words fiance, fiancee sound the same but have different meanings and spellings. Why do fiance, fiancee sound the same even though they are completely different words?
The answer is simple: fiance, fiancee are homophones of the English language.
Alternative spelling of fiancé.
To betroth; to affiance.
Alternative spelling of fiancée.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.