a wireless bridge bridges two networks together. this product typically is a WAP with a built-in hub, which is just a bunch of wired ethernet ports that talk to each other. so near as i can tell, a wireless bridge is exactly equivalent to a WAP + hub, although often is more money.
a wireless router lets all the devices on your network (wireless and wired) talk to the Internet, which is connected to the router through a dedicated port. the neat thing about the router is that everything on your network is hidden from the scary other network; the router is the go-between (it routes packets to and fro) and very often includes a firewall. if you have a DSL or cable connection, this is what you want. wireless routers may also have a few wired hub ports built-in (a la the wireless bridge), and all are routed through the uplink.
NB: you cannot use a router when you need a bridge. if you do, all the devices that connect through the router will appear as one virtual device to the rest of the network. vice versa, the rest of the network won't be able to directly name, let alone connect, to the devices on the router.
NB: if you already have a home network and just want to get your cute little laptop working from the couch without a wire, then you probably just need a WAP. BUT, don't be lured by the routers, even if they are cheaper. you just need a WAP. really.
today's lesson has been made possible by Fry's, which sold me two hubs, a router, and then, about 45 minutes later, a WAP, not all of which i really needed at my parents' house. fortunately, i really do need the router for my home network, so no need to try a Fry's return. and, thanks, Doug, for pointing out the ways in which a wireless network can be hidden and secured.