I grew up calling it one of those two, but a lot of people use the other. I'm trying to find out which is more commonly used.
There was also pa-diddle - played at night, when you saw a car that had only one working headlight.
Definitely "punchy buggy," except for me you'd say "red punch buggy, no punch backs!" The color came first.
There's no "never heard of this game" response. As if I didn't know already, this is just more evidence that I grew up as a very deprived child in a very sick family...