A modem connects

A modem connects
A modem connects your computer to your Internet service provider or ISP. The connection is established through your phone lines. You must have seen a line taken from your phone going into the modem. It simply converts the signals coming from your phone into signals that can be understood by your computer. A router on the other hand assists the connection between computer networks. This device does not do any conversions. It 'routes' signals to a particular network or a computer in the network. Therefore it is called a router. Also read about how does a wireless router work.

Type of Connection
As the router and the modem are establishing a connection between different things, the type of connection they use is also different. The modem connects to the computer (through a router or directly) using a type of connection called RJ45. But it connects to the telephone line through a connection known as RJ11. RJ stands for 'Registered Jack' and its different types are used for different types of network interfaces. The Router on the other hand utilizes only the RJ45 type of connection. This is because it does not have to interact with telephone lines. It deals with computer signals only.

Function
The router vs modem differ in their functionality also. Rather that is the most important difference between them. A modem receives signals from a telephone line which carries analog signals. While delivering this signal to a computer, the modem converts the signal to digital signal. Because a computer can understand only digital signals. This process is known as modulation and demodulation of signals and thus it is called MoDem. Read what does modem stand for? These days cable modems have arrived which work differently. Read what is cable modem. They receive signals from the cables that deliver various channels to your computer. The basic working of the modem still remains same.

The function of a router is to just pass on signals coming from a modem to the right computer network or computer. That is, it just routes data so it is called a router. The router does not perform any conversions but it does filter the data while passing it on. Security measures like firewalls are implemented in the router. Though necessary, a router is not mandatory for establishing an Internet connection. Whereas, a modem is mandatory for an Internet connection. Although, a modem only converts and sends data, so it cannot be used to add security to your network or computer. Also, if you want to use wireless Internet, you have to use a router.

So this was the basic comparison of router vs modem. But you should note that this was only a broad overview and that the topic runs deeper still. There is another comparison, cable modem vs wireless router that talks about a little more details, and you can go through it for more information.