Trams, Trolleys and Streetcars

The real truth is that it's all a spectrum, and the real distinction is between things like different rules for driving vehicles. There's train rules where you have separate ROW and follow signals, and there's tram rules where you're in mixed traffic and operate by sight.
There is one distinctive feature of light rail vehicles, which is the wheel geometry. I think it's largely that light rail wheels are more agressively conical which lets them take way sharper curves. But you can of course just make sure the curves on your tracks are large enough that you don't need these wheels, which is nice because it can apparently tend to start shaking at higher speeds.