Short Version: The modem is a box that connects your home network to the Internet. A router is a box that lets all of your wired and wireless devices use that Internet connection at the same time.
Most ISPs (Internet Service Provider) will give you one box that acts as both modem and router. You can buy them separately. Confusion regularly arises over the fact that the words are often used interchangeably. You need both, integrated in one box or not, in order to provide an Internet connection for all the devices in your home.
Remember the modem, talks to the internet (the WIDE area network) and the router helps translate that to your home or business computer network (the LOCAL area network) so your computers can get on.
If you have a basic setup, a simple combo router/modem provided by your ISP is fine. But if you need really good Wi-Fi then we'd recommend using a separate modem and router. By buying a separate router, you can get what you specifically need for your computing setup. You may need a long WiFi range, or you may need it to be very responsive or just have fast download speeds. If you have mobile devices such as laptops and iPads then you may need long Wi-Fi range.
Modems
A modem modulates and demodulates electrical signals sent through various types of lines and translates incoming analogue signals back into digital data that your computer can understand. Most stand-alone modems have just two connectors - one that connects to the outside world, and an Ethernet port that connects to a computer or a router.
Routers
Your router’s primary responsibility is to route internet data between computers, laptops, tablets and iPads etc in your house, and between those devices and the Internet. The system of connected devices plus the router itself is what we’re meaning when we talk about a "home network" or LAN.
If your router can be within 10 meters of your computers and laptops etc, then a basic router will probably be fine for you. If you have a large home or need faster or more responsive internet (such as for gaming or even Zoom) then you may like a more powerful router. Be aware that the more devices you have on your network (such as laptops, desktops, tablets and phones) the more processing power the router will need as it is working harder and harder to do all the calculations needed to do it's job.
A powerful router will cost anywhere between $300-$600. If you are browsing for a router don't be fooled into thinking that just because it costs more that it's better - I have seen many routers that cost over $500 that did a worse job than the basic model we sell for $130. (This "basic" model is a step up from the router your ISP provided and is fairly grunty and reliable.)
We have another router that we quite like, though we don't sell many, as only people with a very large area to cover need them. They cost around $500, and I have seen it provide signal through 3 walls, past a swimming pool and still provide 3 bars of signal.
If you need any help with your modem or router - if your WiFi or internet isn't everything you want it to be, please give us a call.
Friendly Advice in Plain English. Fast Computer Repairs
0800 FIX NOW
This article by NY Times is good and explains things in more detail. https://www.nytimes.com/wirecutter/blog/modem-vs-router/