220 welder with wrong plug

I'm trying to use a small 220 welder (20amp)at my home, connecting it to my 220 dryer outlet (3 prong). Problem is the welder has the wrong plug. I believe it is considered a 50amp type plug. Best way to describe it is that is looks like a typical 3 prong 110v plug except it is larger and one of the prongs is wider than the other.
Is it possible to make an adapter/extension cord that will mate these two? I bought the appropriate wire from the hardware store (10/3). On the plug end, I bought a dryer type plug. I know the green wire is ground. Does it matter to which prong the other two (black and white) wires go to? The instructions don't make a distinction.
On the socket end of my extension cord, I bought a wall mount type socket than accepts the welder's plug. I assume the middle rounded prong is the ground? Does it matter to which of the other prongs (the wide and narrow) that the white and black wires are connected? I assume it must, but the instructions that came with these products are horrible. On the instructions, the prongs are only labeled x and y, not indicating if the white or black wire should be connected. Thanks