comfort vs calm down

comfort is a noun but calm down is not a noun.

Word	Noun	Adjective	Verb	Adverb
comfort	Yes	No	Yes	No
calm down	No	No	Yes	No

As verbs, calm down is a hyponym of comfort; that is, calm down is a word with a more specific, narrower meaning than comfort:

Other hyponyms of comfort include calm, lull, quiet, quieten, still, tranquilize, tranquillise, tranquillize, allay, ease, relieve, still.

comfort (noun)	calm down (noun)
the act of consoling; giving relief in affliction
assistance, such as that provided to an enemy or to a known criminal
bedding made of two layers of cloth filled with stuffing and stitched together
a feeling of freedom from worry or disappointment
a state of being relaxed and feeling no pain
a freedom from financial difficulty that promotes a comfortable state
satisfaction or physical well-being provided by a person or thing

comfort (verb)	calm down (verb)
lessen pain or discomfort; alleviate	become quiet or less intensive
give moral or emotional strength to	make calm or still
	become quiet or calm, especially after a state of agitation