hand out vs distribute

hand out and distribute both are verbs.

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

As verbs, hand out and distribute are synonyms defined as:

Other synonyms of hand out include give out, pass out.

hand out (verb)	distribute (verb)
give to several people	cause to become widely known
	to arrange in a systematic order
	distribute or disperse widely
	cause to be distributed
	administer or bestow, as in small portions
	give to several people
	release
	be mathematically distributive
	be distributed or spread, as in statistical analyses
	spread throughout a given area