In fact, I borrowed a fluke multimeter, and there is
only about 0.2 Ohm
resistance between the green wire and the case, so that must be the
case ground wire. Do the other two matter much on a 3 prong connector?
Yes, they matter in some cases. Often more in terms of safety than
functionality.
A month or two ago I happened to plug a piece of equipment in which some
dolt (technical term) had connected neutral to ground into an extension
cord that some other dolt had wired with a hot-neutral swap. The results
were nothing short of spectacular on a high current laboratory circuit.
If I knew the identity of either dolt, I think I would teach them the
difference between hot, neutral and ground in a way they wouldn't soon forget.
Eric