admission fee vs price of admission

admission fee and price of admission both are nouns.

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

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

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

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