project vs redesign

project is a noun but redesign is not a noun.

Word	Noun	Adjective	Verb	Adverb
project	Yes	No	Yes	No
redesign	No	No	Yes	No

As verbs, redesign is a hyponym of project; that is, redesign is a word with a more specific, narrower meaning than project:

Other hyponyms of project include engineer, plot, concert, blueprint, draft, draught, map, map out.

project (noun)	redesign (noun)
any piece of work that is undertaken or attempted
a planned undertaking

project (verb)	redesign (verb)
present for consideration, examination, criticism, etc.	design anew, make a new design for
regard as objective
communicate vividly
throw, send, or cast forward
transfer (ideas or principles) from one domain into another
imagine; conceive of; see in one's mind
make or work out a plan for; devise
put or send forth
draw a projection of
cause to be heard
project on a screen
extend out or project in space