Yes, other elements/compounds have fallen into Jupiter over the aeons but even if it was just hydrogen, it is big enough that the pressure alone causes a transition between gas and liquid and farther down solid. There just isn't a set border where you can say that it is one phase on the one side and a different phase on the other. It does more of a slow transition where the gas gets thicker and thicker until at some point you can say it's definitely a liquid instead of a gas, which then gets thicker and thicker until it's not moving anymore.
Similar for Saturn.