A:Answer The modem is the faucet, the router is the "trough" all your devices drink from.
If you're having lag in games, best way to see if it's originating with your provider is to connect a computer directly to the modem, and do some testing that way. If there's no lag connected to the modem, but lag on the router, it could be a failing router.
If you want the best possible performance you can have, first see about turning off the router half of that all-in-one modem/router Xfinity gave you. Turn off everything having to do with DHCP and routing within that thing. Then, connect this router (via hardline) direct to the cable modem, and let THIS device do the routing and wifi source for you. If your ISP connectivity is solid, this device is top notch for ensuring you have no additional problems.