entrance examination vs exam

entrance examination and exam both are nouns.

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

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

entrance examination: examination to determine a candidate's preparation for a course of studies
exam: a set of questions or exercises evaluating skill or knowledge

Other hypernyms of entrance examination include examination, test.

entrance examination (noun)	exam (noun)
examination to determine a candidate's preparation for a course of studies	a set of questions or exercises evaluating skill or knowledge