Home router

In telecommunications networking, a residential gateway (home gateway) allows the connection of a local area network (LAN) to a wide area network (WAN). The WAN can be a larger computer network (such as a municipal WAN that provides connectivity to the residences within the municipality), or the Internet. WAN connectivity may be provided through DSL, cable modem, a broadband mobile phone network, or other connections.

The term "residential gateway" was originally used to distinguish the inexpensive networking devices designated for use in the home from similar devices used in corporate LAN environments (which generally offered a greater array of capabilities). In recent years, however, the less expensive "residential gateways" have gained many of the capabilities of corporate gateways and the distinctions are fewer. Many home LANs now are able to provide most of the functions of small corporate LANs.

Since the early 2000s the residential or home gateway has been used by Telecommunications Multiple Service Operators [MSOs] as a termination device for connecting consumer premises to a broadband delivery network. As a part of the carrier network, the home gateway supports remote control, detection and configuration.

Multiple devices have been described as "residential gateways":

or certain combinations of the above.

A modem (e.g. DSL modem, Cable modem) by itself provides none of the functions of a router. It merely allows ATM or Ethernet or traffic to be transmitted across telephone lines, cable wires, optical fibers, or wireless radio frequencies. On the receiving end is another modem that re-converts the transmission format back into digital data packets.

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Wikipedia