common good vs good

common good and good both are nouns.

Word	Noun	Adjective	Verb	Adverb
common good	Yes	No	No	No
good	Yes	Yes	No	Yes

As nouns, good is a hypernym of common good; that is, good is a word with a broader meaning than common good:

common good (noun)	good (noun)
the good of a community	a raw material that is sold in large quantities, usually to other businesses for manufacturing or production purposes
	benefit
	moral excellence or admirableness
	that which is pleasing or valuable or useful

common good (adjective)	good (adjective)
	having desirable or positive qualities especially those suitable for a thing specified
	morally admirable
	promoting or enhancing well-being
	having the normally expected amount
	with or in a close or intimate relationship
	thorough
	generally admired
	resulting favorably
	not left to spoil
	not forged
	tending to promote physical well-being; beneficial to health
	in excellent physical condition
	appealing to the mind
	agreeable or pleasing
	exerting force or influence
	most suitable or right for a particular purpose
	capable of pleasing
	deserving of esteem and respect
	of moral excellence
	having or showing knowledge and skill and aptitude
	financially safe

common good (adverb)	good (adverb)
	(often used as a combining form) in a good or proper or satisfactory manner or to a high standard (`good' is a nonstandard dialectal variant for `well')
	completely and absolutely (`good' is sometimes used informally for `thoroughly')