The words coin, quoin sound the same but have different meanings and spellings. Why do coin, quoin sound the same even though they are completely different words?
The answer is simple: coin, quoin are homophones of the English language.
A small piece of metal, usually flat and circular, authorized by a government for use as money.
Metal money considered as a whole.
A flat circular piece or object felt to resemble metal money: a pizza topped with coins of pepperoni.
Architecture A corner or cornerstone.
An exterior angle of a wall or other piece of masonry.
Any of the stones used in forming such an angle, often being of large size and dressed or arranged so as to form a decorative contrast with the adjoining walls.
A keystone.
Printing A wedge-shaped block used to lock type in a chase.
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.
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").