The words mordant, mordent sound the same but have different meanings and spellings. Why do mordant, mordent sound the same even though they are completely different words?
The answer is simple: mordant, mordent are homophones of the English language.
Bitingly painful.
Bitingly sarcastic: mordant satire.
Incisive and trenchant: an inquisitor's mordant questioning.
Serving to fix colors in dyeing.
A melodic ornament in which a principal tone is rapidly alternated with the tone a half or full step below.
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").