step forward vs step up

step forward and step up both are verbs.

Word	Noun	Adjective	Verb	Adverb
step forward	No	No	Yes	No
step up	No	No	Yes	No

As verbs, step forward and step up are synonyms defined as:

Other synonyms of step forward include come forward, come out, come to the fore, step to the fore.

step forward (verb)	step up (verb)
make oneself visible; take action	increase in extent or intensity
	speed up
	make oneself visible; take action