The words chili, chilly sound the same but have different meanings and spellings. Why do chili, chilly sound the same even though they are completely different words?
The answer is simple: chili, chilly are homophones of the English language.
The pungent fresh or dried fruit of any of several cultivated varieties of capsicum, used especially as a flavoring in cooking. Also called chili pepper.
Chili con carne.
Cool or cold enough to cause shivering. See Synonyms at cold.
Seized with or feeling cold; shivering.
Distant and cool; unfriendly: a chilly look.
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.