shrug off vs brush aside

shrug off and brush aside both are verbs.

Word	Noun	Adjective	Verb	Adverb
shrug off	No	No	Yes	No
brush aside	No	No	Yes	No

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

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

shrug off (verb)	brush aside (verb)
minimize the importance of, brush aside	bar from attention or consideration