You probably want to use the word "interface" instead of "port" because a port could be a transport layer address, e.g. TCP port 80 is used by HTTP.
Devices don't really have addresses, the addresses are assigned to the interfaces, either physical or logical interfaces. Routers route between networks, so each router interface needs to be in a different network. For Cisco's IOS, you often create logical interfaces (loopbacks, SVIs, etc.), and you assign addresses to those interfaces. Switches can have addresses assigned to SVIs.
When you use a GUI to assign addresses to a device, you are really assigning an address to a particular interface of the device. I assume you mean something like a home router (off-topic here). A home router will usually have two router interfaces (WAN and LAN), and each of those interfaces get assigned to a different network, and the router routes traffic between the networks. The LAN interface of a home router may be a logical interface to which a switch module and WAP connect inside the chassis.