carpet pad vs underlay

carpet pad and underlay both are nouns.

Word	Noun	Adjective	Verb	Adverb
carpet pad	Yes	No	No	No
underlay	Yes	No	Yes	No

As nouns, carpet pad and underlay are synonyms defined as:

Other synonyms of carpet pad include rug pad, underlayment.

carpet pad (noun)	underlay (noun)
a pad placed under a carpet	a pad placed under a carpet

carpet pad (verb)	underlay (verb)
	provide with a base, support, lining, or backing
	put (something) under or beneath
	raise or support (the level of printing) by inserting a piece of paper or cardboard under the type