Phillips screws/bits are designed to cam out above a certain torque, because torque limiting automatic tools didn't exist at the time. The folks who developed Phillips suddenly realized this was a really dumb idea, because it was relatively easy to develop torque limiting power screwdrivers and the cam-out tendency damages the screw.
My understanding is that Pozidriv was then invented by the same folks to solve this problem. Unfortunately, Phillips had already been established as an industrial standard in the states so we never really changed. Europe, on the other hand hadn't totally transitioned from slotted screws yet and so they effectively standardized on Pozidriv.
JIS screws also do not cam out and look far more like Phillips than PZ -- there's a little dot on the head that identifies them. JIS screws can take a lot more torque than Phillips and will strip easily if you use a Phillips driver. AFAIK the bits are only made in Japan by Japanese tool companies.
Everything that joeswamp says is pretty much spot on!
Phillips screws were already being used in the U.K. when Pozidriv was introduced, but mainly in areas such as the aviation industry! They remain standard in the British aviation industry to this day, but are a rarity!
I'm just old enough to remember when Pozidriv were introduced in the U.K. (about 1970 if I recall). The design was heavily pushed by GKN, if I recall correctly, and by the late 70's the Phillips had pretty much disappeared!
Pozidriv Sizes are 0 to 4 inclusive, but 0 and 4 are rare! Only place I can recall seeing No.4 Pozi's are the door hinges on some BMC cars! These days it would be a Torx! Sizes 1,2 and 3 are everywhere, and probably 50% of the screws I turn are No.2 Pozi.
Just about every European manufacturer of anything uses Pozidriv rather than Phillips, and I don't even carry, Phillips in my 'go bag'! Exceptions are anything aircraft or aero engine related, electronics and electrical equipment, and most optical stuff!