The words coy, koi sound the same but have different meanings and spellings. Why do coy, koi sound the same even though they are completely different words?
The answer is simple: coy, koi are homophones of the English language.
Tending to avoid people and social situations; reserved.
Affectedly and usually flirtatiously shy or modest. See Synonyms at shy1.
Annoyingly unwilling to make a commitment.
Ornamental domesticated varieties of the common carp, Cyprinus carpio, of Japan and eastern Asia with red-gold or white coloring
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.