press on vs progress

press on is not a noun while progress is a noun.

Word	Noun	Adjective	Verb	Adverb
press on	No	No	Yes	No
progress	Yes	No	Yes	No

As verbs, progress is a hypernym of press on; that is, progress is a word with a broader meaning than press on:

Other hypernyms of press on include advance, go on, march on, move on, pass on.

press on (noun)	progress (noun)
	the act of moving forward (as toward a goal)
	gradual improvement or growth or development
	a movement forward

press on (verb)	progress (verb)
continue moving forward	develop in a positive way
	form or accumulate steadily
	move forward, also in the metaphorical sense