A fare is a transportation fee. Ferries, taxis, and airplanes charge their passengers fares. We use "fee" for charges for services that don't involve transportation. Doctors, lawyers, dentists, etc. charge fees.

Fare is used for the price of transport eg bus fare, train fare, metro fare Fee is used for the price of a professionals services eg lawyers' fees, or for the entrance fee to a facility like a museum or swimming pool.