Real Dictionary

third class in American English
noun: the class, grade, or rank immediately below the second

third class in British English
of the class or grade next in value, quality, etc, to the second
noun: the class or grade next in value, quality, etc, to the second

third-class
A third-class degree is the lowest honours degree that can be obtained from a British university.
In the past, the third-class accommodation on a train or ship was the cheapest and least comfortable accommodation.

third-class in American English
of the class, rank, excellence, etc. next below the second
with accommodations next below the second class
adjective: of the lowest or poorest class or quality; inferior
adverb: by third-class mail or passenger accommodations