entrance fee vs price of admission

entrance fee and price of admission both are nouns.

Word	Noun	Adjective	Verb	Adverb
entrance fee	Yes	No	No	No
price of admission	Yes	No	No	No

As nouns, entrance fee and price of admission are synonyms defined as:

Other synonyms of entrance fee include admission, admission charge, admission fee, admission price, entrance money.

entrance fee (noun)	price of admission (noun)
the fee charged for admission	the fee charged for admission