I know that there are wired routers, and wireless routers. Do wired routers do the same thing as wireless routers, without wireless capabilities?
Most if not all wireless routers also work wired! Nearly all of them have at least four wired ports. The access point is the wireless connector, it just connects wireless capable machines to the exact same point within the router as the wired plugs do. A Wired router does not have the internal access point. With a wired router you can add wireless ability by simply adding an access point to them. The AP (access points) cost about as much as a full wireless router so you don't see them used very often but they are available. All the wireless does is eliminate the need for a local cable. Really that's all it does. Any computer connected to a router is connected to the router, wired or wireless makes no difference, although as a general statement the wired machines will be faster! So yes wired and wireless routers do exactly the same thing, they route local traffic for several machines to one broadband connection.
You are correct. Generally these days your typical router will have one input port (to the Internet) and four output ports, one or more of which can be connected to other computers -- while also having wireless capability. Wiring directly to the router is useful for desktops, servers, and other hardware that may not have wireless capability, while also eliminating any interference that could be associated with wireless routing, such as radio interference or downtime.
