Simple Java Client/Server Program
It's probably a firewall issue. Make sure you port forward the port you want to connect to on the server side. localhost maps directly to an ip and also moves through your network stack. You're changing some text in your code but the way your program is working is fundamentally the same.
There is a fundamental concept of IP routing: You must have a unique IP address if you want your machine to be reachable via the Internet. This is called a "Public IP Address". "www.whatismyipaddress.com" will give you this. If your server is behind some default gateway, IP packets would reach you via that router. You can not be reached via your private IP address from the outside world. You should note that private IP addresses of client and server may be same as long as their corresponding default gateways have different addresses (that's why IPv4 is still in effect) I guess you're trying to ping from your private address of your client to the public IP address of the server (provided by whatismyipaddress.com). This is not feasible. In order to achieve this, a mapping from private to public address is required, a process called Network Address Translation or NAT in short. This is configured in Firewall or Router. You can create your own private network (say via wifi). In this case, since your client and server would be on the same logical network, no private to public address translation would be required and hence you can communicate using your private IP addresses only.
If you got your IP address from an external web site (http://whatismyipaddress.com/), you have your external IP address. If your server is on the same local network, you may need an internal IP address instead. Local IP addresses look like 10.X.X.X, 172.X.X.X, or 192.168.X.X.
Try the suggestions on this page to find what your machine thinks its IP address is.