Is WAN ip address and PUBLIC ip address the same?

Yes it is if you're talking about your home router connected to an ISP.You get a public, routable IP address from your ISP that is associated with the WAN interface on your router.

In a corporate network they're usually not the same. A WAN on a router is its Wide Area Network interface and can be used for a private circuit (T1, DS3, etc) between 2 or more locations. In that case the WAN IP addresses will not be public.

What is meant by public IP address is an address that can be used on the Internet. There are private IP addresses (192.168.x.x, 10.x.x.x and 172.16.x.x) that you can't use on the Internet

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Yes.Both are same. To find out what is your WAN or public IP address from one side and what is your internal, router or LAN IP address from other side check out IP trackers:

http://www.ipaddresslocation.org/

http://www.find-ip-address.org/

They will show you all about your computer.

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If I understand what you're additionally asking, you would be able to would desire to establish port forwarding on your router. additionally, carry out a traceroute/tracert on your IP to verify the place the relationship is breaking. consistent with threat your ISP is obstructing inbound connections? additionally, some routers would have a putting to not respond to pings, have you ever checked this on your router settings?