Device What is does
 Gateways: Convert information from one format to another.
  • The proper technical term for a DSL, FiOS, or Cable modem is a gateway because, with DSL and cable, the data remains in a digital format from the customer's network to the ISP and internet.     
        
  • Since the digital data is not converted to an analog data, the device is technically not a modem.
              
  • However, since calling a DSL/cable gateway a modem is a term many people easily understand, it the 2 terms are used interchangeably.
  • Typically, routers today will perform the functionality of both a router and a switch - that is, the router will have multiple ethernet ports that devices can plug into.
  • In a similar vein, combination modem/routers are actually typically performing the roles of a gateway, a router, and a switch.
 Modem: Stands for modulating demodulating.

They allow devices to communicate with other remote devices by converting digital data into analog data and transmitting it over an analog telephone line.
 Routers: Are responsible for sending data from one network to another.
 Switches: They use the MAC address of a device to send data only to the port the destination device is plugged into.
 Hubs: Unlike switches, hubs broadcast data to all ports, which is inefficient.

Note: modern voice system will require your network to have a router in it. Despite the fact that some modems have integrated router features, they barely capable of maintaining voice systems functionality. You may want to have both modem and router in your network (modem will need to  be launched in bridged mode).