OK, here goes. Bill, you probably already know this, but there are some reading this board that do not, so I will be overly simple for their benefit.

In the "old days" dryers and ranges had two "hot" wires, and a third that served both as a ground, and as a 'neutral' for incidental 120v. loads (light, timer, etc.) On these machines, there was a strap that connected the case of the appliance to the third wire.

For a variety of reasons (too involved to get into here), we separate the "ground" from the "neutral" back at the main panel. Simply put, the neutral wire is intended to always be carrying current, and to become "hot" if it comes loose.... while the ground is never intended, under normal circumstances, to be carrying current. It's just there, in case something bad happens.

So, dryers and ranges now get plugs with four prongs, and, in the case of romex, are hooked up to four wires. These units DO NOT have the case connected to the "neutral."

The correct solutions are:
1) The guy with the four-wire plug gets to run a four-wire cable to his outlet, and replace the receptacle; and,

2) The guy with the three-wire plug gets to replace it with a four wire cord..AND remove that 'bonding' strap in the back of the appliance.

This is one situation where it will 'work' even if it's NOT OK.