be vs fall under

be and fall under both are verbs.

Word	Noun	Adjective	Verb	Adverb
be	No	No	Yes	No
fall under	No	No	Yes	No

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

Other hyponyms of be include make, compose, constitute, form, make, range, straddle, fall into, pose, present, supplement.

be (verb)	fall under (verb)
spend or use time	be included in or classified as
work in a specific place, with a specific subject, or in a specific function
have an existence, be extant
have life, be alive
form or compose
have the quality of being; (copula, used with an adjective or a predicate noun)
occupy a certain position or area; be somewhere
be identical to; be someone or something
be identical or equivalent to
represent, as of a character on stage
be priced at
to remain unmolested, undisturbed, or uninterrupted -- used only in infinitive form