slide down vs fall in

slide down and fall in both are verbs.

Word	Noun	Adjective	Verb	Adverb
slide down	No	No	Yes	No
fall in	No	No	Yes	No

As verbs, fall in is a hypernym of slide down; that is, fall in is a word with a broader meaning than slide down:

Other hypernyms of slide down include break, cave in, collapse, founder, give, give way.

slide down (verb)	fall in (verb)
fall or sink heavily	break down, literally or metaphorically
	become part of; become a member of a group or organization
	to take one's place in a military formation or line