The words chin, chine sound the same but have different meanings and spellings. Why do chin, chine sound the same even though they are completely different words?
The answer is simple: chin, chine are homophones of the English language.
The central forward portion of the lower jaw.
To pull (oneself) up with the arms while grasping an overhead horizontal bar until the chin is level with the bar.
Music To place (a violin) under the chin in preparation to play it.
To chin oneself.
Nautical The line of intersection between the side and bottom of a flatbottom or V-bottom boat.
The backbone or spine, especially of an animal.
A cut of meat containing part of the backbone.
A ridge or crest.
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").