Real Dictionary

second class in American English
noun: the class of travel accommodations, as on a train, that are less costly and luxurious than first class but are more costly and luxurious than third class

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

second-class
If someone treats you as a second-class citizen, they treat you as if you are less valuable and less important than other people.
If you describe something as second-class, you mean that it is of poor quality.

second-class in American English
of the class, rank, excellence, etc. next below the highest; of secondary quality
adjective: of a secondary class or quality
adverb: by second-class mail or passenger accommodations

second-class in British English
adjective: cheaper than first class
noun: second-class accommodation on a train or ship