Jupiter is far from being a star
Jupiter would have to be 80 times more massive than it is to ignite fusion processes and become a star. So I would say Jupiter and the rest of the Jovians in our Solar System at least certainly fall into the planet category.
This is not to say, though, that some of those monster exoworlds out there might just be brown dwarfs after all. Of course, one could ask just what the heck is a brown dwarf - a gray middle ground between true planets and true stars? Oh, why doesn't the Universe just give us some straight answers?!