Modem
A modem converts between the provider's access technology and data usable by your local networking equipment. Cable and some DSL services commonly use devices called modems.
ONT
Fiber-to-the-home service commonly terminates at an optical network terminal (ONT), which converts the provider's optical access connection to an interface used by the home network.
Router
A router forwards traffic between your home network and other networks. Consumer routers also commonly provide NAT, DHCP, firewall functions, Ethernet switching and Wi‑Fi.
Gateway combo units
ISPs often supply a gateway that combines the access termination and router/Wi‑Fi functions. That is convenient, but it can make it harder to tell whether a problem belongs to the provider link, routing function or wireless coverage.
Bridge/passthrough concepts
Some users choose to use a separate router behind an ISP gateway. Product-specific bridge or passthrough settings differ substantially, so consult the provider and device documentation rather than copying generic settings from another model.