shrug off vs dismiss

shrug off and dismiss both are verbs.

Word	Noun	Adjective	Verb	Adverb
shrug off	No	No	Yes	No
dismiss	No	No	Yes	No

As verbs, dismiss is a hypernym of shrug off; that is, dismiss is a word with a broader meaning than shrug off:

Other hypernyms of shrug off include brush aside, brush off, discount, disregard, ignore, push aside.

shrug off (verb)	dismiss (verb)
minimize the importance of, brush aside	declare void
	bar from attention or consideration
	end one's encounter with somebody by causing or permitting the person to leave
	cease to consider; put out of judicial consideration
	terminate the employment of; discharge from an office or position
	stop associating with