The modem is what provides a connection to your Internet Service Provider, or ISP. It grabs that connection and holds on to it, allowing you to access the outside world, also known as the internet. Modems do not provide any type of security or networking, they are not smart. They simply open a door to the internet and allow any device that is connected to the modem to send and receive files through the internet.
The router does something different, it is smart. The router creates a network that all of your devices can access to communicate with each other within your home or office. This can be through a wired connection or through a WiFi connection. That network between your devices works with or without the modem. Without the modem, the router can not access the internet. When you connect the router to the modem, it then can give all of your devices access to the internet while still protecting your network.
... Wait, there's modems with built in routers?? Yes! This is what usually confuses people about the difference between modem and router. I'll explain. There are modem/router combos. They still operate like having both devices would, but you only have to see one box. This is great for people who want to reduce clutter or want to ditch wires as much as possible.
Ditch that modem rental fee!
Check which devices are supported by your ISP and click the appropriate link below to go purchase one at Amazon. They usually have the best prices for them and the easiest return policy. Just in case!
Here's some pictures of the equipment you typically need to make your internet work. Don't worry, all of this is included when you receive a modem. These images are used as reference to help you understand modem vs router appearance. Your materials might look a little bit different, so I'll explain the parts that make each piece of equipment important.