VTA light rail

You also have Caltrain, which is a proper S-Bahn running from downtown San Francisco all the way to downtown San Jose, with then some select trains continuing onward to Gilroy.

But you also have the very large Muni light rail system running all throughout San Francisco itself, San Jose has a light rail system of its own, the much more bland and highly suburbanized VTA light rail.

There's the Altamont Corridor Express, which goes from San Jose all the way into Stockton and may actually be part of a future expansion of service, the Valley Link, I believe.

You have Amtrak's Capital Corridor, which runs from mostly Oakland to Sacramento and actually kind of provides some local connectivity of its own in the Berkeley area.