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A class that is not a set (informally in Zermeloโ€“Fraenkel) is called a proper class,
and a class that is a set is sometimes called a small class.
For instance, the class of all ordinal numbers, and the class of all sets,
are proper classes in many formal systems.

In Quine's set-theoretical writing, the phrase "ultimate class" is often used
instead of the phrase "proper class" emphasising that
in the systems he considers, certain classes cannot be members,
and are thus the final term in any membership chain to which they belong.

Outside set theory, the word "class" is sometimes used synonymously with "set".
This usage dates from a historical period where classes and sets
were not distinguished as they are in modern set-theoretic terminology.