step up vs step forward

step up and step forward both are verbs.

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

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

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

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