relay vs put across

relay is a noun but put across is not a noun.

Word	Noun	Adjective	Verb	Adverb
relay	Yes	No	Yes	No
put across	No	No	Yes	No

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

Other hypernyms of relay include communicate, pass, pass along, pass on.

relay (noun)	put across (noun)
the act of passing something along from one person or group to another
electrical device such that current flowing through it in one circuit can switch on and off a current in a second circuit
a race between teams; each member runs or swims part of the distance
a crew of workers who relieve another crew
a fresh team to relieve weary draft animals

relay (verb)	put across (verb)
pass along	transmit information
control or operate by relay