This article explains the difference between router and modem. It is a common convention among home users to address their wireless routers as modems which is incorrect. The fundamental difference between a router and modem is explained.
A modem is a device which is used to convert your analog signal to digital signal and vice versa. In the below diagram, there is an internet connection at home. A PC which requires connection to the internet, connect to the modem which would then connect to the wall socket. Note that, the job of the modem is only to convert the digital signals generated by the PC to analog signal which is then forwarded to the ISP. So how does the internet work in this scenario ?
The PC connects to the ISP using appropriate credentials like username / password which is provided by the ISP. Once the ISP successfully authenticates the credentials, the PC gets a public IP address assigned by the ISP. This public IP address , which is your identity on the internet would help you to connect to the internet.
A router is a device, which is used to share the internet among multiple users. But again, routers does not have the functionality of converting analog to digital signals. For this, a modem is required. Routers have the option to have modems inbuilt in them or as an additional device.
The below diagram shows a router which is connected to a modem, which in turn is connected to the internet. The router is used predominantly for sharing the internet among multiple users on the network and also provides additional functionality like wireless connectivity, VPN, Security Etc. When a router is used, the username / password credentials provided by the ISP is configured on the router, which would then connect to the internet. Once successful, the router would receive a public IP address from the ISP. This IP address would then be shared among all the users on the network by using a feature available on the router called NAT.
From the above explanation , it can be understood that routers and modems are different from each other and each has its own functionality.
So to access internet, you would need a modem and for providing additional features, a wireless router is used along with an additional or inbuilt modem.