speed vs push forward

speed is a noun but push forward is not a noun.

Word	Noun	Adjective	Verb	Adverb
speed	Yes	No	Yes	No
push forward	No	No	Yes	No

As verbs, push forward is a hyponym of speed; that is, push forward is a word with a more specific, narrower meaning than speed:

Other hyponyms of speed include barge, thrust ahead, buck, charge, shoot, shoot down, tear, dart, dash, flash, scoot, scud, shoot.

speed (noun)	push forward (noun)
changing location rapidly
a central nervous system stimulant that increases energy and decreases appetite; used to treat narcolepsy and some forms of depression
a rate (usually rapid) at which something happens
the ratio of the focal length to the diameter of a (camera) lens system
distance travelled per unit time

speed (verb)	push forward (verb)
move faster	push one's way
cause to move faster
move very fast
travel at an excessive or illegal velocity
move hurridly