display vs acting out

display and acting out both are nouns.

Word	Noun	Adjective	Verb	Adverb
display	Yes	No	Yes	No
acting out	Yes	No	No	No

As nouns, acting out is a hyponym of display; that is, acting out is a word with a more specific, narrower meaning than display:

display: exhibiting openly in public view
acting out: (psychiatry) the display of previously inhibited emotions (often in actions rather than words); considered to be healthy and therapeutic

Other hyponyms of display include array, screening, showing, viewing, sight, fanfare, flash, ostentation, flaunt, presentation.

display (noun)	acting out (noun)
something shown to the public	a (usually irritating) impulsive and uncontrollable outburst by a problem child or a neurotic adult
a visual representation of something	(psychiatry) the display of previously inhibited emotions (often in actions rather than words); considered to be healthy and therapeutic
an electronic device that represents information in visual form
exhibiting openly in public view
something intended to communicate a particular impression
behavior that makes your feelings public

display (verb)	acting out (verb)
to show, make visible or apparent
attract attention by displaying some body part or posing; of animals