break up vs break away

break up and break away both are verbs.

Word	Noun	Adjective	Verb	Adverb
break up	No	No	Yes	No
break away	No	No	Yes	No

As verbs, break away is a hyponym of break up; that is, break away is a word with a more specific, narrower meaning than break up:

break up (verb)	break away (verb)
laugh unrestrainedly	break off (a piece from a whole)
break or cause to break into pieces	flee; take to one's heels; cut and run
come to an end	move away or escape suddenly
separate (substances) into constituent elements or parts	withdraw from an organization or communion
cause to go into a solution	interrupt a continued activity
cause to separate
close at the end of a session
bring the association of to an end or cause to break up
make a break in
set or keep apart
break violently or noisily; smash
attack with or as if with a pickaxe of ice or rocky ground, for example
release ice
destroy the completeness of a set of related items
take apart into its constituent pieces
suffer a nervous breakdown
disband
to cause to separate and go in different directions
discontinue an association or relation; go different ways