downhearted vs downcast

downhearted is not a noun while downcast is a noun.

Word	Noun	Adjective	Verb	Adverb
downhearted	No	Yes	No	No
downcast	Yes	Yes	No	No

As adjectives, downhearted and downcast are synonyms defined as:

Other synonyms of downhearted include blue, depressed, dispirited, down, down in the mouth, gloomy, grim, low-spirited, low.

downhearted (noun)	downcast (noun)
	a ventilation shaft through which air enters a mine

downhearted (adjective)	downcast (adjective)
filled with melancholy and despondency	filled with melancholy and despondency
	directed downward