I thought trolley was the british word for that very same vehicle.
Nope. The only trolleys we have are shopping trolleys. I used to be a trolley boy at a supermarket, and would collect and move trolleys in the car park.
For the vehicle that ThatDarkNinja just posted, we would probably call that a Tram.
For larger vehicles that don't have overhead wires, they're all trains, whether steam, petrol or electric.