The words coquet, coquette sound the same but have different meanings and spellings. Why do coquet, coquette sound the same even though they are completely different words?
The answer is simple: coquet, coquette are homophones of the English language.
To engage in coquetry; flirt.
To trifle; dally.
A woman who makes teasing sexual or romantic overtures; a flirt.
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.