As a Stockholmer born and raised, and considering the fact that Stockholm is the only Swedish city to yet have a subway system, I feel it's my duty to introduce you to some some slang words having to do with tunnelbanan.
Tuben. (noun, definite) A loan-translation of the British expression "the tube" with the same meaning.
Tricken. (noun, definite) Also a nickname for tunnelbanan.
Planka. (verb) To be fare-dodging or gatecrashing, i.e. riding without a ticket
So... there's that. Congratulations on learning a couple of slang words. :p
In Sweden, Stockholm is the only city to have built a subway system. But if you're sleeping there, probably some guards will come wake you up. :p Nonetheless, on late weekend nights you can always find a few unlucky drunk people who fell asleep on their way home and got way too far...
In this sentence, the feeling I get is that "tunnelbanan" is used as a general noun for the subway system as a place where one can be.
But you can also use it to refer to a train, although personally I think I'd prefer "ett tunnelbanetåg" ("subway train"). But that's just my personal preference. For just one car, it's "tunnelbanevagn" ("subway car").
If it's already obvious that you're talking about the subway, you can of course say just "vagn" and "tåg".