link up vs join

link up is not a noun while join is a noun.

Word	Noun	Adjective	Verb	Adverb
link up	No	No	Yes	No
join	Yes	No	Yes	No

As verbs, join is a hyponym of link up; that is, join is a word with a more specific, narrower meaning than link up:

As verbs, link up and join are synonyms defined as:

Other synonyms of link up include connect, link, unite.

link up (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

link up (verb)	join (verb)
make a logical or causal connection	make contact or come together
connect, fasten, or put together two or more pieces	cause to become joined or linked
be or become joined or united 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