This subject came up a little while ago, in a thread about Thomas the tank engine. This is what I posted at the time.
Yes, Thomas is British or, at least, his creator was. But the idea that the word "railway" is British and "railroad" American has come about by a peculiar accident of history.
The first "inter-city" line in the world was between Manchester and Liverpool. In 1825 a Bill was presented to Parliament to authorise the construction of the Liverpool and Manchester Railroad. There were serious inaccuracies in the details of this Bill and it was rejected. The following year, a revised Bill was presented to Parliament. Parliamentary rules, I believe, would not allow a "second chance" to a Bill that had already been rejected in that session. So the new Bill, which became an Act of Parliament, was for construction of the Liverpool and Manchester Railway.
This may be an over-simplified version of history, but at the time the terms railway and railroad were interchangeable. BTW I notice that there are many "railways" in the US.
HTH - Peter
There are many other examples:
switches (USA); points (UK) - so I use the word junctions instead
trucks (USA); bogies/bogeys (UK)
passenger cars (USA); carriages or coaches (UK)
freight train (USA); goods train (UK)
ETM (end of train marker); FRED (flashing rear end device)