stretch forth vs gesture

stretch forth is not a noun while gesture is a noun.

Word	Noun	Adjective	Verb	Adverb
stretch forth	No	No	Yes	No
gesture	Yes	No	Yes	No

As verbs, gesture is a hypernym of stretch forth; that is, gesture is a word with a broader meaning than stretch forth:

Other hypernyms of stretch forth include gesticulate, motion.

stretch forth (noun)	gesture (noun)
	motion of hands or body to emphasize or help to express a thought or feeling
	something done as an indication of intention
	the use of movements (especially of the hands) to communicate familiar or prearranged signals

stretch forth (verb)	gesture (verb)
thrust or extend out	show, express or direct through movement