The words coat, cote sound the same but have different meanings and spellings. Why do coat, cote sound the same even though they are completely different words?
The answer is simple: coat, cote are homophones of the English language.
A sleeved outer garment extending from the shoulders to the waist or below.
A garment extending to just below the waist and usually forming the top part of a suit.
A natural outer covering, such as the fur of an animal; an integument.
A layer of material covering something else; a coating: a second coat of paint.
A small shed or shelter for sheep or birds.
Obsolete To go around by the side of; skirt.
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.