So I recently started watching Bucky's Computer Networking tutorial and at the 26th episode he explains how IP adresses work and how you can find out your own Network IP, how many host your network can have, etc. 
So I wanted to try this with my own IP but then I came across something confusing for me. When I googled what my IP adress was I got a different IP than when I looked on my system to find my IP adress. I  then logged into my modem/router (it's apparently a modem and a router in one) and saw both IP adresses. The one I googled was apparently a WAN IP adress and the IP my system told me was a LAN IP adress. Now my question is: What is the difference between those and which one do I need to find out my Network IP. 

Thanks in advance, 

This is the video I'm talking about by the way :)