Well, modem is a very specific device but can be loosely defined as the device that connects you to your ISP. Sometimes the modem is in your house and sometimes it's outside the house. I'm not familiar with FIOS, but I'm sure their "router" is proprietary to their service which handles the networking to their servers. I'll take a stab in the dark and assume the router uses cellular technology to connect rather than phone lines or tv cable. But it's basically exactly the same thing as a modem/router for all intents and purposes.
I was just saying for the people that have Verizon FIOS, they only have to worry about a router since there is no modem like Cable service has. One less box to have worry about buying/renting or replacing when it goes down.
FYI, in case Verizon FIOS becomes available to you.
There's no modem in the FIOS system. A device called an (Fiber) Optical Network Terminal (ONT box) converts between light and electrical signals. It's a big box with a laser in it that they nail to your house.
The router is a normal router, except that it has an added feature: a MoCA (Multimedia over Coax Alliance) interface, in addition to the usual Ethernet jacks. This might make it look like a cable modem, but it's not.
The ONT has an Ethernet jack that you can connect to any router. The trick is in getting Verizon to set you up to use it. Their standard procedure nowadays is to instead run a single coax line from the ONT to a splitter, and from there to the MoCA-capable router, using that line for both TV and data. (The phone line is run separately.) They don't do this to lock you into using their router, per se, though it has that effect since it is needed for TV Guide and on-Demand. They do it to save on wiring (one less line to run), and because it makes for an easy upgrade for people with existing cable modem systems.
I have 2 FIOS lines, one for Business Internet with Static IPs and one for Home TV. On the Internet side, I use my own Wireless N Router since it is Internet only and connects via Ethernet. On the Home side, I use there router since it connects via coax and need it for the TV guide and on-demand.