Alright, the difference is ip addresses on your network are handed out by your router. More than likely you are using DHCP. That means that whenever a computer joins your network or powers on, a new ip address will be given to it. These are your local ip addresses. They are local because of the way that ip works. The rest of the world only sees your external ip addresses, and your router, and other computers on your network only see the local ip addressess.
There is a finite amount of ip numbers, so to solve this, areas of the internet are broken up into smaller networks, on those networks all outside communication comes and goes through one point. Everything behind this point can have ip address that is used and reused all over the world because that address only deals with traffic on that specific network. It is similar to having a 12 Broadway street in London, and one in Boston. To have mail delivered to 12 Broadway in London all of the mail goes to England then London, then finally goes to Broadway. It doesn't just go directly to broadway. You can think of your router as being the London post office. From there it sends the mail to your PC, which has a IP number that is more than likely also used on my network.
What you are trying to do, isn't what you should be doing. What you want to do is use LAN play. Because everyone you are trying to play with is on the same LAN (local area network) i.e. everyone is on the same network. Try doing that, and see if everything works with no complications. If you run into any, do a google search of the error message or the problem and see if you can come up with the answer.
If you do want to play with people that aren't on your network or a combination of the two, that is when you would be using direct ip. With that, the people trying to connect on your network would use the local ip address of your computer, (which can change when you power off by the way, unless you set up a static IP, which is something you need to do if you plan to use the direct IP conncection to play with people off of your network.) and the people not on your network would use your external ip address. Although the people playing on your LAN, could probably use the external ip address too ...not sure if that would work or not, in theory it would. If this is what you are trying to do, you will need to set up a static ip address, and port forwarding.
To find out what your external ip address is, you need to go into your router settings. To find out how to do that, go to your router's manufacturer website. I believe it is Linksys. Basically you are going to be putting your router's local ip address into the url address bar in a browser. You might need to use a PC that is connected with a ethernet cable directly to the router to do this. You will also need the password and stuff. If you haven't changed it from the default username and password, you can also find that info on the Lynksys website. This would be a good time to tell you, you really, I mean really, REALLY need to change your default username and password on your router. Also, somewhere in the settings of the router is an option to not allow access to the router settings except by a PC directly connected, i.e. through a cable. If this isn't already setup this way, I believe it is just a box you have to check, do so, it should be a setting somewhere in there, not sure how it is exactly worded. You can figure it out though, just might have to read a little. After you have done all of that, your external ip address will be listed somewhere in there.
As far as setting up an external ip address, google just that, how do I set up a static ip address. I am not going to repeat info that is listed all over the place, it is a waste of everyone's time as you can find pages that have nice photos and all that. As far as the port forwarding goes, currently I am trying to find out which ports I need forwarded also. So I can't help you there, but I will tell you that in the router settings is where you are going to be setting up the port forwarding to the static ip address you have set up. Just google how to set up port forwarding with you routers model number ...you know the one you listed before, and you will find guides on it.
I hope that helps.
