leave vs fall out

leave is a noun but fall out is not a noun.

Word	Noun	Adjective	Verb	Adverb
leave	Yes	No	Yes	No
fall out	No	No	Yes	No

As verbs, fall out is a hyponym of leave; that is, fall out is a word with a more specific, narrower meaning than leave:

leave: move out of or depart from
fall out: leave (a barracks) in order to take a place in a military formation, or leave a military formation

Other hyponyms of leave include depart, go, go away, pop out, file out, get off, hop out, get off, step out, eject, undock, log off, log out.

leave (noun)	fall out (noun)
the act of departing politely
permission to do something
the period of time during which you are absent from work or duty

leave (verb)	fall out (verb)
leave unchanged or undisturbed or refrain from taking	come to pass
be survived by after one's death	have a breach in relations
leave behind unintentionally	drop out
go and leave behind, either intentionally or by neglect or forgetfulness	leave (a barracks) in order to take a place in a military formation, or leave a military formation
move out of or depart from	come as a logical consequence; follow logically
go away from a place
leave or give by will after one's death
transmit (knowledge or skills)
put into the care or protection of someone
remove oneself from an association with or participation in
produce as a result or residue
make a possibility or provide opportunity for; permit to be attainable or cause to remain
act or be so as to become in a specified state
have left or have as a remainder