The words apatite, appetite sound the same but have different meanings and spellings. Why do apatite, appetite sound the same even though they are completely different words?
The answer is simple: apatite, appetite are homophones of the English language.
A natural, variously colored calcium fluoride phosphate, Ca5F(PO4)3, with chlorine, hydroxyl, or carbonate sometimes replacing the fluoride. It is a source of phosphorus for plants and is used in the manufacture of fertilizers.
An instinctive physical desire, especially one for food or drink.
A strong wish or urge: an appetite for learning.
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").