These look almost identical, but the long pin is on the wrong side... So then I ordered a different kind of 20 amp plug... The kind that looks like a 15 amp plug with one of the pins at 90 degrees.

Same problem... The outlet has the 90 degree pin on the wrong side...

Where are you located? I'm not sure what you are talking about.

20 amp receptacles have been around quite awhile now and so have their plugs.

Can you attach pictures so I can see what you have.

Canada... How do I attach pictures?

What voltage are we dealing with?
Sounds like you got the wrong one. You need to figure out the NEMA number and work that way.

Yes - I think I've figured out that Cisco keep sending me 220 Volt cables and all my outlets are 120V... I have both the twist lock and straight connectors, but Cisco;s are the opposite to mine.