bar examination vs exam

bar examination and exam both are nouns.

Word	Noun	Adjective	Verb	Adverb
bar examination	Yes	No	No	No
exam	Yes	No	No	No

As nouns, exam is a hypernym of bar examination; that is, exam is a word with a broader meaning than bar examination:

bar examination: an examination conducted at regular intervals to determine whether a candidate is qualified to practice law in a given jurisdiction
exam: a set of questions or exercises evaluating skill or knowledge

Other hypernyms of bar examination include examination, test.

bar examination (noun)	exam (noun)
an examination conducted at regular intervals to determine whether a candidate is qualified to practice law in a given jurisdiction	a set of questions or exercises evaluating skill or knowledge