A wireless router usually has 1 to 3 wired ports. If there is an area of your home or office where you cannot get a strong signal from a wireless adapter, you could connect, via CAT5 ethernet wire, an wireless access point to the wireless router. Under this circumstance, one has a wireless router and a wireless access point.
Typically, a wireless router offers more than a wireless gateway (AP). It allows more clients and also usually doubles as a print server for the network. SMC 7004ABWR and DI-713P are two examples.
However, if one already has a wired router, adding an Access Point, to be wired into the router, offers a wireless capability to an existing wired network. I have an SMC7004BR router connected to a desktop PC, a DSL modem, an HP printer and an Orinoco RG-1100 Gateway setup as an access point. On another floor, there is another desktop and a laptop, both using wireless adapters to communicate with the router via the RG-1100. This was cheaper and more flexible than replacing the router with a wireless version.