The devices you are talking about (standard consumer grade WiFi routers that enable WiFi access to an ISP's DSL or cable service) have multiple integrated functions that act at different layers and it may help you understand if you think about that layering.
The Wireless Interface is Layer 1 - the physical carrier that is in this case a shared RF environment. There are a host of standards (802.11 abgnhw...) that deal with the specifics. This is by its very nature a shared medium, possibly with multiple concurrent channels, possibly with individually encrypted sessions, but where communications are almost always directly between individual end points and the wireless access point. The Wifi protocols handle the physical signalling that are used to encapsulate the next layer, which is typically ethernet. While wireless AP's do switch traffic in the sense that a processor coordinates the stream of traffic between two nodes rather than relying on dumb rebroadcasting the fact remains that the WiFi environment is a shared medium and many of the characteristics of switching in the wired world simply do not apply to WiFi.
That leads to the next part of the system - a wired Ethernet switch. This is a layer 2 device that allows Ethernet packets to be sent directly from a source to a destination as identified by MAC addresses. The Ethernet packets received by the WiFi radios in the AP are fed into the same switch and can be switched (not routed yet) to any other port on that switch, that may be one of the wired interfaces or another wireless client.
The final layer involved is the router part - this may be more or less a basic ethernet router that allows traffic to be moved from the switch to the external network and vice versa. You will see that most of these devices default to a private address space for the WiFi and switch connected devices (e.g. 192.168.1.x) and traffic has to be routed to move from that network to the external interface (DSL\cable modem, whatever) that will have a public ip-address provided by an ISP or some other upstream network.