If by gateway you mean WAN, no.
That summary page doesn't show everything.
The WAN IP address *should* be the external IP address assigned by your ISP, the one taken directly from the modem. The Router IP address should be the IP address the router has assigned itself in order to act as a gateway managing your network. Usually the default is 192.168.0.0 or some such (e.g. the address you use to access the router management tool). The router will also have a subnet mask somewhere. It is acting as a DHCP server - in other words, it dynamically assigns IP addresses to machines that access it on a local network, but filters outgoing traffic through a single external IP address (the WAN address). Each time your laptops and desktops (and printers, if they have network functionality) start up and access the router for a session, they retrieve an IP address, subnet mask, gateway, and DNS server addresses from the router. This gives them all the information they need to access your local network, which the router reinterprets so you access the external network (internet).
This is providing you have the DHCP server turned on. If it's turned off, you must manually assign the information to the TCP/IP settings of each functional Network Connection to match up with the router's subnet mask, gateway, and DNS servers (the IP will be identical but for the last 3 digits). Turning off the DHCP server and not configuring the client machines accordingly will kill internet access, but it would typically do it for all conncections, not just wireless (unless of course the wired connection in your laptop is still carrying IP settings which match up to the router, which I kinda doubt).
One other thing: the MAC addresses you see there are unique hardware identifiers, and many routers have MAC address filtering as an additional means of security (which should only be used as security when coupled with WPA or WPA2). Make sure you didn't turn that on. Next time you post a screenshot though you can leave the IP's undarkened (nobody cares what you external and internal IPs are here, and they can't really do much with it, though if you're really paranoid you can black the WAN address; the internal one we need to see) and black out the MAC addresses.
So, your list of to do's:
-Hardware reset.
-Power cycle.
-Delete any bridged connections.
-Post the results of the ipconfig /all command.