US perspective from doing a lot of train and subway travel. "Station" and "stop" refer to different things.
A station is a building where people embark and disembark, wait for trains or greet arriving passengers, possibly buy tickets, etc.
A stop is a location where people embark and/or disembark. A station would normally be a stop, but a stop isn't necessarily at a station.
As a practical matter, every underground subway stop has to be a station.
It isn't unusual for train stops to be at just a platform with little in the way of improvements beyond rain cover and benches, especially for local, above ground commuter train stops.
At one time, it was possible for someone to disembark from inter-city trains at a standard stopping point in the middle of nowhere in a rural area. I suspect that is no longer done, both for liability reasons and because you can't manage a modern train service if you allow those kinds of stops.