Can my friend and I play Minecraft with different IP's?

Your question is a bit ambiguous, do you mean the following:

You've made a server, and it's running on your computer or another on your home network

Your friend is not at your house, he's at his house and he wants to join your server.

If so then the answer is yes, he can (has to) use your external IP address to join, and you can (have to) use your local IP address. If the server is on the same computer that you're running Minecraft on then rather than use your 192.168.x.x address you either use 127.0.0.1 or 'localhost' instead.

As long as you are running multiplayer, I see no reason why not. I had a MC server with one external, and one internal IP playing at the same time (1.7.4). However, I think both were connecting via the external IP then through the port forwarding....

Some routers have issues with LAN going out to Internet and coming back into the same LAN via an external IP. No idea why, but there seems to be a few of those routers out there (there is no reason why it cannot work).

This all assumes the MC server is on a separate PC, not either of the gaming users! It is when the MC server and player are on the same machine that those routers get confused when routed by external IP - a conflict in shortest route/path....

Solution is to always run the MC server on a dedicated PC, one that is not being used to play as a user.

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