lead by the nose vs lead astray

lead by the nose and lead astray both are verbs.

Word	Noun	Adjective	Verb	Adverb
lead by the nose	No	No	Yes	No
lead astray	No	No	Yes	No

As verbs, lead astray is a hypernym of lead by the nose; that is, lead astray is a word with a broader meaning than lead by the nose:

lead by the nose: conceal one's true motives from especially by elaborately feigning good intentions so as to gain an end
lead astray: cause someone to believe an untruth

Other hypernyms of lead by the nose include betray, deceive.

lead by the nose (verb)	lead astray (verb)
conceal one's true motives from especially by elaborately feigning good intentions so as to gain an end	cause someone to believe an untruth
	lead someone in the wrong direction or give someone wrong directions
	teach immoral behavior to