Since the old thread on turning a Pi into a router has been locked, I can't correct some errors that were posted in it.
A "router" is to a "bridge" as a "switch" is to a "hub".
A hub takes any packet it receives and sends it out to all of it's other ports,. A switch checks the address on each packet and sends it to only the port that has the destination address. If the packet doesn't go to any device connected (even indirectly) to one of it's ports, it will be sent to it's uplink port. So...a switch is the "smart" version of a hub. Also note that switches can be connected in cascade. Hubs cannot.
Likewise, a bridge takes any packet that arrives on one of its two ports and sends it out the other port. A switch checks the address on each packet and only sends packets to the other port if the destination is not on network it came from. So...a router is a "smart" bridge.
A router (or bridge) generally has two connections (even in the SOHO market there are "deal-WAN" routers with one local and two WAN ports). Many SOHO routers come with a built-in switch, typically with 4 ports. (I once owned a pre-Cisco Linksys with an 8 port switch.) Many modern routers also include a switch capability to handle wireless connections. SOHO routers also typically provide additional services, the common one being DHCP.
It used to be that switches were very expensive and hubs were--relatively--cheap. These days, it's problaby very difficult to even *find* a hub. You are also very unlikely to actually encounter a bridge.
Now all of that said, one of the features o the typical broadband modem with a built-in router and switch, is the ability to "bridge" the "router". That is just turning off all routing activities and making it a simple pass-through device...a bridge. If a facility has a fixed block (usually a static one), then one can connect a switch to a bridged router, assign the devices static IP addresses, and then you have direct, public routing. The more common arrangement is to bridge the ISP_supplied "router" (really a modem-router-switch) and connect your own router to it. That way, you can have a router under your full control at all times, instead of one that may have hidden "features" that you don't want and can't turn off.