Suzy,
The star that "shouldn't exist" is a proper, giant star, nothing like Jupiter (by size, surface temperature and power output). The problem/issue with it is a lack of "metals" from it's chemical composition - it should have have more of them, but it doesn't.
Jupiter may be called a "failed" star, because it didn't have a chance to acquire enough mass to start thermonuclear fusion in it's core.
Apart from that, we can define planets in very different terms.. but this will not change the current definition imposed by IAU
