A modem is the device that allows your home to access the internet. You can connect computers and tablets, TVs and other devices directly to the modem by using ethernet cables. However, it is most common to hook up a router, which will create a Wi-Fi signal throughout your home.
Cable modems plug into the cable TV line, meaning that you can bundle internet and cable TV services together. Meanwhile, DSL modems use telephone lines. DSL connections cap out at slower speeds than cable connections do, but they are more widely available. The fastest internet connection available uses fiber-optic technology. Fiber-optic cables send light-based signals, so information travels at light speed.
Finally, Voice over Internet Protocol (VoIP) modems are not differentiated by the way they connect to the internet but rather by how they incorporate an analog phone line. A VoIP modem pairs an analog telephone adaptor with either a DSL or cable modem, allowing you to hook up a landline phone to the internet without having to purchase a separate VoIP telephone adaptor.