At present most of the equipment provided by Internet service providers have the functionality of performing the function of a router and a modem, so it could be called a modem, router or modem-router.
Features of a Modem
Modems without router functionality are characterised by operating via Dial UP connections and do not have additional functionality coming from a router. Such as the DHCP service.
In the 1990s and early 2000, what was used to use the connection were modems. That’s why a lot happened that you could not talk on the phone while using the Internet connection.
Those are not the modem types that exist. There are also cable modems that work by means of Internet technology known as “DOCSIS” by means of a coaxial (telecable) cable line. An example of this is the Motorola SBG 900 cable modem that only works the connection on a single computer even if you put a switch to have more than one entry because it has no DHCP service.
Characteristics of a router
A router is physically characterised by not having an RJ11 port (Input to connect a telephone line cable) and instead of that input has an RJ45 that through that it reaches the connection from the Internet.
Routers become very necessary when you have more than one computer on a network. Because each of these computers needs to be assigned a local IP address through a DHCP service. Which is a function that the routers have. Therefore you can not simply put a switch because it does not have the DHCP function.
Any questions you have about the differences of a modem and a router please leave a comment.