Trolley is like a 'train', it is on steel tracks. A trolleybus is a bus that is hooked up to wires, which power the trolleybus, above. Google image search is your friend.
It should be, "We're riding the trolley." Nobody says, "...going by trolleybus," unless the trolley goes 100s of kilometers. Trolleys only go short distances.
Trolleybuses, as well as so called "shared taxis", which are indeed small buses going on pre-defined routs, are not common to many countries. This fact creates misunderstanding and confusion among the DL community. It would be very helpful if the creators of this unit used pictures to introduce the words for those means of public transportation, which are unique to Ukraine.