Well, they do two separate things and can be bought separately or together in one device. A modem is a device that translates electronic signals so the computer can communicate with the world, most of the time thru the internet. It can do this through the phone line or through a broadband connection. A router is a device that, like the name implies, routers signals to where they are supposed to go. It can also split an internet connection so that multiply computers can access the internet at once. Also, (most importantly for me) it acts as a hardware firewall to protect your computers. But, to answer the meat of your question, it depends on how you are going to be connecting to the internet. If you are using dial up, then you only need a modem ( a phone/fax modem). You will actively be using your phone line (which means that you cannot talk on the phone and be online at the same time) and yes, you will have to dial out and connect to your ISP (internet service provider) If you are using broadband, then you will have a "always on" connection to the internet. This means that you will not have to dial out or login to anything to use the internet. As soon as your computer is on, then you are connected to the internet. You will also need a modem to use this service but will need a different kind of modem. The two most common are a cable modem (works thru your cable tv) or DSL (which is thru your phone line, but you can still be online and talk on the phone at the same time). Most people that have multiply computers have broadband and use it with a router so that each computer has a "always on" fast internet connection. Now some ISP that provide broadband will send you just a modem and some will send you a modem and a router in one. I highly recommend to get a router if you are going to get broadband, even if you have one computer, because of the hardware based firewall.
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Feras Abualrub , Web Solutions Manager , Qistas for Information Technology
A modem is the device that allows computers to send data over a phone/cable line. A router is a device that is used to create a home network. It has a section that assigns IP addresses to computers that connect to it. It also has the ability to connect to modems. Using a router will enable you to connect multiple computers to the internet at the same time.
