brooding vs melancholy

brooding and melancholy both are nouns.

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

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

brooding (noun)	melancholy (noun)
persistent morbid meditation on a problem	a humor that was once believed to be secreted by the kidneys or spleen and to cause sadness and melancholy
sitting on eggs so as to hatch them by the warmth of the body	a feeling of thoughtful sadness
	a constitutional tendency to be gloomy and depressed

brooding (adjective)	melancholy (adjective)
deeply or seriously thoughtful	grave or even gloomy in character
	characterized by or causing or expressing sadness