- For Teachers
It's simply another variety of World English that you may not be used to, apparently British-English.
Slang is unrelated.
They are neither slang nor dialect, unless you can feel you can reasonably use those words to describe basic terminology common within a given industry. Yes, there are many slang terms used in railroading, but the terms in question are not slang: they simply and clearly describe what is happening.
The facts: To be on a departing train, we need to know when it leaves this station, not when it arrives at its destination. Similarly, to meet a train, we don't care when it left the distant station, only when it arrives here. For time given at this station to refer to what's happening at the distant station wouldn't make much sense or be at all useful.
Time used in reference to a train refers to the time of whatever event is occurring at this station:
"The 9:12 to Anytown" is the train departing this station for Anytown at 9:12.
"The 9:12 from Anytown" is the train arriving at this station from Anytown at 9:12.