Router hookup to modem question

The round connector on the back of her modem is for a coax cable connection for an internet source - like a cable company or the feed from her satellite box. A modem delivers an internet signal and shares it with a computer or a network connected to computers. The modem should also have a network socket (maybe more than one) that will be used to feed the signal into a router (either wired or wireless) to distribute internet to a network or just one PC through a network cable from the modem to the PC. The phone like connector she sees on her router is a network connection - larger than the plug or socket used for a telephone. There has got to be more than the "round connector" on that modem. Or she is looking at a satellite box that would only have coax connectors - in and out - and that then needs a modem to connect to via coax and then out to the pc or router via network cable. If all that is there is the coax connector(s) she does not have a modem.

It is highly unlikely anyone has a phone modem any longer - while it would still work on a phone dialup connection, it would work VERY slowly.