nut vs pull together

nut is a noun but pull together is not a noun.

Word	Noun	Adjective	Verb	Adverb
nut	Yes	No	Yes	No
pull together	No	No	Yes	No

As verbs, pull together is a hypernym of nut; that is, pull together is a word with a broader meaning than nut:

Other hypernyms of nut include collect, garner, gather.

nut (noun)	pull together (noun)
a small (usually square or hexagonal) metal block with internal screw thread to be fitted onto a bolt
one of the two male reproductive glands that produce spermatozoa and secrete androgens
someone who is so ardently devoted to something that it resembles an addiction
a whimsically eccentric person
usually large hard-shelled seed
half the width of an em

nut (verb)	pull together (verb)
gather nuts	assemble or get together