Modem is short term for Modulator-demodulator. It is involved in the process of connecting home PCs to internet. Router is also involved in connecting your home PC to internet. It is a networking device.
Modulation is the process of changing one or more properties of the carrier signal with a modulating signal containing information to be transmitted.Demodulation is the process of extracting the signal having information from modulated carrierwave.So, to encode digital information, a modem modulates the signal and to decode the information that was transmitted, it demodulates the signal. On the other hand, the information collected by the modem is directed to devices within the network by a Router.It makes sure that the information reaches to its desired destination and it restricts the information to be exposed to any other devices other than the destination. This is very important to maintain this job on a large network where the volume of data is enormous.
Basically, Modem is responsible for bringing in the information. Router is responsible for distributing (“routing”) the information to different devices such as computers or phones.
It works on the Layer 1 of OSI (Open Systems Interconnection) model i.e. the physical layer which is responsible for conveying the bit stream across the network. It works on the Layer 3 of OSI model i.e. the network layer. This layer is responsible for providing switching and routing technologies.
There are two ports in a Modem.One is used to connect to the Internet Service Provider and the second port is used to connect to the router in case of large network. There are typically four ports in a router. The number of ports in a router can be 2, 4 or 8.
Modem is inter-networking device. Router is a networking device.
Modem can be connected to a PC using the Ethernet port. Router can be connected to a number of computers or other networking devices using the Ethernet cables or Wi-Fi.
Internet connection is a necessity for modem. It is not necessary to have internet connection for routing. But to allow multiple connections and enhanced security, internet connection is needed.
Modem does not have any security measures.Data does not get screened by a modem while encoding or decoding. Therefore, there is a threat to the computers connected to the modem. To protect the network, router facilitates security measures.It screens data packets to figure out their destination. So a router can contain firewalls to protect devices from attacks on the network.
Typically, a modem sends and receives data through telephone lines. It is used to connect one PC or the whole home computer network to the ISP. Router helps the computers to get connected to the modem and to one another in the network.The packets of information delivered by a router are selective.
Modems can be categorized in the following ways;·

  • Based on Directional Capacity::   Half duplex modem and   Full duplex Modem
  • Based on Connection to the line :   2-wire modem and 4-wire modem
  • Transmission Mode :Asynchronous Modem and Synchronous Modem
There are various types of Routers available viz. :·

  • Broadband Routers :Wireless Routers, Edge Routers, Subscriber Edge
  • Subscriber:  Inter-provider Border Router, Core Router and  Wired & Wireless Routers
The price of a modem can vary from $5 to $23,000 depending upon the features, brand and functionality The price of a router can vary from $10 to $74,000. The price depends upon the brand, style, features and functionality.
Some of the companies that make modems are:Huawei, Cisco, Netgear, D-Link, Telebit. Some of the companies that make routers are:Cisco, Linksys, Netgear, Lucent, HP, D-Link.