The words coal, cole, kohl sound the same but have different meanings and spellings. Why do coal, cole, kohl sound the same even though they are completely different words?
The answer is simple: coal, cole, kohl are homophones of the English language.
A natural dark brown to black graphitelike material used as a fuel, formed from fossilized plants and consisting of amorphous carbon with various organic and some inorganic compounds.
A piece of this substance.
A glowing or charred piece of solid fuel.
Charcoal.
See kale.
A cosmetic preparation, such as powdered antimony sulfide, used especially in the Middle East to darken the rims of the eyelids.
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").