stretch out vs gesture

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

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

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

Other hypernyms of stretch out include gesticulate, motion.

stretch out (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 out (verb)	gesture (verb)
stretch (the neck) so as to see better	show, express or direct through movement
thrust or extend out
extend one's body or limbs
extend or stretch out to a greater or the full length
lie down comfortably