fios delivers fiber to the box outside your house, then coax carries it into and through your house. You connect a modem to the coax. The modem is required to separate the internet "channels" from the rest of the signal being carried over the fiber/coax cable, a router alone will not do that.

That modem either has an ethernet port that you use to connect it to a router or is built into a router if the router is rented from the provider. The router distributes the internet signal throughout the house (usually wirelessly though you can use ethernet if you have one of the tiny percentage of houses that have ethernet wiring).

Think about it this way, the time between the advent of home internet service and wireless were almost completely simultaneous. High speed internet to the home became available en mass in the mid to late 90s, wireless in the late 90s. So, the idea of having wired network distribution (ethernet) in the home was only a thing for about 5 years. Almost no one did that. Plus fios didn't exist as a service until after wireless became a thing. Thus if fios needed that, the cost of the wiring would have prevented fios from getting any market share.