In British English, "underground" refers to any subterranean railway. The "tube" is, in strict usage, only the deep-level part of the "underground", that is the part of the network built in the 1890s and later, which to save money, had to fit the narrowest diameter tunnels capable of being fitted with standard (4 foot, 8.5 inch) track. This required very coaches set very low on their wheels, with rounded roofs, from which, when they stop at platforms also used by normal rolling stock, passengers have to step up six inches or so, instead of stepping down.
Much of the pre-1890 "underground"network is known as the "Metropolitan line." This gave its name to the circa 1900 subterranean railway in Paris, where it came to be abbreviated as "Metro", and is used in Montreal, Mexico City, Brazil, Santiago de Chile and elsewhere, and often, not just for subterranean railways, but also (e.g. in Recife, Brazil) for any railway, surface or subterranean, serving a city centre and its immediate outskirts.
"Subway" in British usage means an subterranean path for "tramcars" (street cars) or pedestrians (e.g. to provide a safe way to cross under a busy street).
Your list of foreign words for subterranean railways omits the "Subterráneo" of Buenos Aires, shortened to "subte."
If I am writing for British readers, I use "underground" for any subterranean railway, anywhere. If I am writing for North American readers, I use "subway" similarly for any subterranean railway. If I expect readers from both places, I would probably use "metro." In the only foreign language I ever write in (Portuguese) I would also opt for "metro."
Obviously if it were necessary to distinguish a particular line, then I would say "S-Bahn" or "Red Line" or "Circle Line" as appropriate, but such a choice would be made within the clearly stated context of Berlin, Washington DC, London etc.