finish up vs finish

finish up is not a noun while finish is a noun.

Word	Noun	Adjective	Verb	Adverb
finish up	No	No	Yes	No
finish	Yes	No	Yes	No

As verbs, finish is a hypernym of finish up; that is, finish is a word with a broader meaning than finish up:

Other hypernyms of finish up include complete.

As verbs, finish up and finish are synonyms defined as:

Other synonyms of finish up include end up, fetch up, land up, wind up.

finish up (noun)	finish (noun)
	the act of finishing
	a decorative texture or appearance of a surface (or the substance that gives it that appearance)
	(wine tasting) the taste of a wine on the back of the tongue (as it is swallowed)
	designated event that concludes a contest (especially a race)
	the downfall of someone (as of persons on one side of a conflict)
	event whose occurrence ends something
	the place designated as the end (as of a race or journey)
	a highly developed state of perfection; having a flawless or impeccable quality
	the temporal end; the concluding time

finish up (verb)	finish (verb)
finish a task completely	finally be or do something
finally be or do something	come or bring to a finish or an end
	cause to finish a relationship with somebody
	finish eating all the food on one's plate or on the table
	provide with a finish
	have an end, in a temporal, spatial, or quantitative sense; either spatial or metaphorical