It's a cut. However, in flatland cities where the train was there first there's no railroad engineering reason to have a cut. It's done only for grade separation purposes. For some reason, "trench" has become the standard term for that, at least around CA since the Alameda Corridor did it. Was Alhambra done before Alameda, and if so when?

It's rare because a bridge or a fill is easier and cheaper to build and better for the railroad (no vertical clearance problems with bridges, no need to pump it out all the time if groundwater is high). The locals (read NIMBYs these days) don't like that, though, because they can still see the railroad if it's elevated and the noise does carry farther. Locals would prefer a tunnel of course but that's usually out of the question. For current discussions on the issue see the SF Peninsula high speed rail items here and in the newsline. Same basic reasoning for why a rail transit subway is usually preferred to elevated by locals though not by those who have to pay for it.