melancholy vs sadness

melancholy and sadness both are nouns.

Word	Noun	Adjective	Verb	Adverb
melancholy	Yes	Yes	No	No
sadness	Yes	No	No	No

As nouns, sadness is a hypernym of melancholy; that is, sadness is a word with a broader meaning than melancholy:

Other hypernyms of melancholy include unhappiness.

melancholy (noun)	sadness (noun)
a humor that was once believed to be secreted by the kidneys or spleen and to cause sadness and melancholy	the quality of excessive mournfulness and uncheerfulness
a feeling of thoughtful sadness	emotions experienced when not in a state of well-being
a constitutional tendency to be gloomy and depressed	the state of being sad

melancholy (adjective)	sadness (adjective)
grave or even gloomy in character
characterized by or causing or expressing sadness