the internet is a wan.

The internet is a WAN because, through the use of ISPs, it connects lots of smaller local area networks (LANs) or metro area networks (MANs). On a smaller scale, a business may have a WAN that's comprised of cloud services, its headquarters, and smaller branch offices.

The WAN port in a WiFi router is essentially connecting you to the real "internet". The cable coming out of modem, or if a PPPoE connection, a simple RJ45 ethernet cable are to be plugged in the WAN port. The WAN cable transmits the data from Internet to "Subnet" created by your router.

A wide area network is a geographically distributed private telecommunications network that interconnects multiple local area networks (LANs). Typically, a router or other multi function device is used to connect a LAN to a WAN.