Japan operates a kind of hybrid system where the subway (at least in Tokyo) mostly consists of tracks that connect to private operators on either end, and a train will just run through from the private parts of the track to the subway parts with no interruption whatsoever.

https://en.wikipedia.org/wiki/List_of_through_trains_in_Japa...

In the United States, probably the best comparison would be BART in San Francisco Bay Area and WMATA in Washingon, D.C. area. They act like a subway in city center, and like a (commuter) railway outside. As a stretch, also look at SF Muni Metro which acts like a tramway/streetcar outside the dense areas, else like a "light subway" in the dense areas.

The line gets really blurry in some places in Tokyo.

Asakusa (one of "my" lines!) line, is definitely a subway inside central Tokyo, but you can stay on the same physical train going all the way from Narita to Haneda (think RER in Paris?) — I think it would be qualified as "light rail" anywhere else in the world.