price of admission vs entrance fee

price of admission and entrance fee both are nouns.

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

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

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

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