I have two IP addresses, as expected: I have my "internal" IP address, as do all other computers on my lan, and my "external" IP address attributed to my router and which is visible to the internet.
Now if something/someone wants to connect to my computer here, then they need to connect via my router first (using my external IP address). Whatever port that application is trying to connect on needs to be forwarded to my internal IP address by the NAT table set up on the router. Any attempts to connect to me via a port that's not set to come to my computer explicitly, won't connect.
If you're both behind routers, then you'll both need to make sure you have the appropriate ports forwarded properly in order to connect to each other.
Now if something/someone wants to connect to my computer here, then they need to connect via my router first (using my external IP address). Whatever port that application is trying to connect on needs to be forwarded to my internal IP address by the NAT table set up on the router. Any attempts to connect to me via a port that's not set to come to my computer explicitly, won't connect.
If you're both behind routers, then you'll both need to make sure you have the appropriate ports forwarded properly in order to connect to each other.