sadness vs melancholy

sadness and melancholy both are nouns.

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

As nouns, melancholy is a hyponym of sadness; that is, melancholy is a word with a more specific, narrower meaning than sadness:

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

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