third-class mail vs third class

third-class mail and third class both are nouns.

Word	Noun	Adjective	Verb	Adverb
third-class mail	Yes	No	No	No
third class	Yes	No	No	No

As nouns, third-class mail and third class are synonyms defined as:

third-class mail and third class: mail consisting of printed matter qualifying for reduced postal rates

third-class mail (noun)	third class (noun)
mail consisting of printed matter qualifying for reduced postal rates	inexpensive accommodations on a ship or train
	mail consisting of printed matter qualifying for reduced postal rates