Phillips and JIS are very similar. As I understand it, JIS was only sufficiently different from Phillips to avoid paying royalties to Phillips Screw, or their successors. They have now changed the pattern so newer Japenese screws are interchangable with Phillips. You only really need JIS to work on older Japanese cars and bikes. A JIS driver will fit a Phillips screw (though not as well as the proper driver) but not vice versa.
Pozidriv are totally different. They are NOT interchangable with anything (apart from Supadriv which is really only a variation). Phillips screws were designed for the first generation of mechanical drivers, and they simply 'cam out' of the screw when it's done up, which works, but isn't ideal.
Pozidriv are designed not to do that, and were designed for torque controlled screwdrivers. It's a much better design, and should have replaced Phillips instantly, but didn't. Size for size, a Phillips driver will fit inside a Pozidriv recess but there's a load of slop and it won't grip well. A Pozidriv driver will not fit a Phillips recess, unless you drop a size, which doesn't really work either!
Strangely, Pozidriv was an instant success in the U.K. which hadn't really adopted Phillips anyway, and you will hardly ever find Phillips screws here, other than in the aviation industry which has used them for years. Ditto most of Europe.
I notice the difference. Probably 95 % of the cross head screws I drive are Pozidriv. My PB Swiss drivers are generally a superb fit and I get loads of torque. If I encounter a Phillips (generally only on Japanese cars) and it's a bit rusted in, I find the things really frustrating as I have to push the driver so hard!