lie down vs stretch out

lie down and stretch out both are verbs.

Word	Noun	Adjective	Verb	Adverb
lie down	No	No	Yes	No
stretch out	No	No	Yes	No

As verbs, stretch out is a hyponym of lie down; that is, stretch out is a word with a more specific, narrower meaning than lie down:

Other hyponyms of lie down include stretch, charge, bow down, prostrate.

lie down (verb)	stretch out (verb)
assume a reclining position	stretch (the neck) so as to see better
	thrust or extend out
	extend one's body or limbs
	extend or stretch out to a greater or the full length
	lie down comfortably