outburst vs acting out

outburst and acting out both are nouns.

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

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

outburst: an unrestrained expression of emotion
acting out: a (usually irritating) impulsive and uncontrollable outburst by a problem child or a neurotic adult

Other hyponyms of outburst include cry, explosion, flare.

outburst (noun)	acting out (noun)
a sudden violent disturbance	a (usually irritating) impulsive and uncontrollable outburst by a problem child or a neurotic adult
an unrestrained expression of emotion	(psychiatry) the display of previously inhibited emotions (often in actions rather than words); considered to be healthy and therapeutic
a sudden intense happening