hand out vs portion out

hand out and portion out both are verbs.

Word	Noun	Adjective	Verb	Adverb
hand out	No	No	Yes	No
portion out	No	No	Yes	No

As verbs, portion out is a hyponym of hand out; that is, portion out is a word with a more specific, narrower meaning than hand out:

Other hyponyms of hand out include apportion, deal, divvy up, share.

hand out (verb)	portion out (verb)
give to several people	give out as one's portion or share