The router can help with dividing the internet only. Without modem, users of the router cannot access to the Internet.But it’s not the only difference between router and modem.
Modem, as an AccessPoint, cannot create a new IP address. For example, if the IP is 192.168.10.1 so, all the connected computers will run under the same IP.
But the Router can create new IP address from the original one. For example, it raises a 192.168.10.2 based on the source. Another IP address means another LAN.