The router allows you to configure the network. This device has its own IP address and can assign addresses to network participants, depending on the settings. The modem does not have its own address, IP is assigned directly to the computer (its network card), and connecting two or more devices is impossible without connecting a router or software routing.
The functionality of routers depends on the device model. Some of them are able to work as a firewall, thus increasing the level of network security. As a rule, routers (including modem routers) have several interfaces for connecting terminals (computers and other devices, including wireless ones. In the latter case, the term “access point” is used). The number of ports also depends on the model and class of the device. A modem without a router function allows you to connect one terminal.
Routers, unlike modems, even when working with a single connected computer, perform the tasks of assigning a dynamic IP address (DHCP) and transmitting IP packets (NAT). In the latter case, we can talk about security, since the IP address of the computer assigned to the data packet is replaced by the external IP assigned by the provider by the router to the server.