fall in vs slide down

fall in and slide down both are verbs.

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

As verbs, slide down is a hyponym of fall in; that is, slide down is a word with a more specific, narrower meaning than fall in:

Other hyponyms of fall in include go off, implode, buckle, crumple, flop, break, sink, slump.

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