The words faerie, faery, fairy sound the same but have different meanings and spellings. Why do faerie, faery, fairy sound the same even though they are completely different words?
The answer is simple: faerie, faery, fairy are homophones of the English language.
A tiny, mischievous, imaginary being; a fairy.
The land or realm of the fairies.
Obsolete spelling of fairy.
A tiny imaginary being in human form, depicted as clever, mischievous, and possessing magical powers.
Offensive Slang Used as a disparaging term for a homosexual man.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, 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.
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").