Modems and routers are different in the sense that a modem is used to modulate and demodulate (hence the name) a signal, like an analog phone line or DSL. A router is a device meant to route traffic from one source to another, like from a PC to the internet. These days, modems and routers are integrated into a single appliance that often also has firewalling built-in. Those other boxes might very well be firewalls, PoE switches etc. rather than just routers.
17 minutes ago, MojangYang said:
Now we have one of those routers that connects to to the look-like-Ethernet-port-but-I-don’t-think-it-is port (the other end of the looks-like-Ethernet port is connected to a nbn box in the garage that is also connected to a fibre-optic cable). Can somebody tell me what is that port?