The two major components of the system that gets your home computer or mobile connected to the internet are the modem and the router. The modem communicates with your Internet Service Provider’s network. It is called a cable modem if it connects to your cable provider through a coaxial cable. It is a DSL modem if it is connected to your telephone line. Your modem will necessarily depend on the ISP’s infrastructure capability. It could be fibre or satellite also.
The router shares this internet connection among the various devices in your home or office. If it is wireless and creates a Wi-Fi network the devices can connect to. The router may be provided with ports for Ethernet cables. The router connects to the Internet, through the modem and is the recipient and owner of a single IP address on the internet, which servers on the net can connect to.
Routers come with firewalls which are protective barricades against the internet and offer protection in the hardware format in addition to the software firewall protection available on your computer.
ADSL devices combine both in one piece of equipment.
All brands of modems and routers basically work the same way except for a few cosmetic differences.
But there is a range of modems and routers to choose from and the prices vary from 30 dollars to a few hundreds
When choosing a modem, if your service provider is providing internet through the cable network, the modem for cable is a standard one called the DOCSIS 3.0 being the latest format across all brands. If it is a DLS connection, you would go for a VDSL connection for speeds greater than 15 Mbps and an ADSL connection for lesser speeds.