IP geeks, please help me on this!

11) We have a remote terminal connection that we use to access our server from an offsite place, I was troubleshooting a problem and I had set the IP address (statically) as its supposed to be, later on I found out that I was using the wrong IP address and I don’t know how yet I had connected to my sever and I even went through the Linux username prompt stage. We have the server IP address and the internet modem IP address. My problem is I can’t get my real IP address. I have entered the IP addresses to my Browser so that I can access the router and they both go through but there is something am not sure of, am I on giant network that’s why I have an IP address or how is that set up.?
Example:
Router IP and the internet Modem IP address) 55.55.555.51
The other IP address (WAN?) 55.55.555.52
