put together vs join

put together is not a noun while join is a noun.

Word	Noun	Adjective	Verb	Adverb
put together	No	No	Yes	No
join	Yes	No	Yes	No

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

Other hypernyms of put together include create, make.

put together (noun)	join (noun)
	a set containing all and only the members of two or more given sets
	the shape or manner in which things come together and a connection is made

put together (verb)	join (verb)
create by putting components or members together	make contact or come together
	cause to become joined or linked
	become part of; become a member of a group or organization
	come into the company of
	be or become joined or united or linked