Damocles for the win...........
Video explaining the difference...
How did I never know this before?
Great video!
Here's an image (from Google) of a proper mating of a JIS screw and its appropriate driver:
If I get around to it, I'll share an image of a bad fit between a Phillips bit and a JIS screw.
All this said, the nuclear solution mentioned by lineman1234 above (cutting a flat-blade slot into a screw head with the assistance of Mr. Dremel Moto-Tool) often proves effective (don't ask me how I know this!).
Confessing, my most recent experience with slot-cutting; I wrongfully used a hex bit in a Torx (or is it, torque?) head screw; boogered the screw head terribly. Had to unleash the Moto-Tool and its fearsome swift cut-off disk to solve the problem. Now, gotta find a proper torque-head replacement screw!
OK, here's what a bad fit between a Phillips head screwdriver and a JIS screw looks like::
Hope image appears; don't know why only a URL appeared in my attempt at posting a picture earlier in the post.