Technically not. Stacja is where train stops , dworzec is a building, or all of the infrastructure.
So if you are talking about a builing it is "dworzec", if it's a small station with no buildings, it's "stacja"
If you are talking about a place where you take the train, but it's not a middle of nowhere you use both interchangeably.
>I thought of "przystanek" as a tram or bus stop.
And that's how many people think about them. I never use trains, but the first time I've seen somebody calling its stop „przystanek” was in an article which, among others, explained the train terminology and clarified "incorrect" common usage. This name does makes sense, if you need very accurate terms for the elements of the train station.
>Would the stops on the Warsaw metro be a przystanek as well as a stacja?
I've just searched for „przystanek metra” out of curiosity. It turns out that indeed, you can use „przystanek” for the place where metro train stops for passengers. „Stacja” is also good.