Modem vs router: different jobs, different problems.

The modem

On cable internet, the modem communicates with the provider’s DOCSIS network and hands Ethernet to a router.

The router

The router creates the local network, routes traffic, and often provides Wi-Fi. Poor room-to-room coverage is therefore usually a router or access-point problem, not a modem problem.

The gateway

A gateway combines both functions. That is convenient, but it can make troubleshooting less obvious because several roles live in one box.