entrance exam vs exam

entrance exam and exam both are nouns.

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

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

entrance exam: 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 exam include examination, test.

entrance exam (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