The words chic, sheik sound the same but have different meanings and spellings. Why do chic, sheik sound the same even though they are completely different words?
The answer is simple: chic, sheik are homophones of the English language.
Conforming to the current fashion; stylish: chic clothes; a chic boutique.
Adopting or setting current fashions and styles; sophisticated: chic, well-dressed young executives. See Synonyms at fashionable.
The quality or state of being stylish; fashionableness.
Sophistication in dress and manner; elegance.
Islam A religious official.
Islam A leader of an Arab family or village.
Islam Used as a form of address for such an official or leader.
Slang A romantically alluring man.
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").