When configured as a modem only it would indeed be a bridge, assuming it lets you configure it to be so. (I believe it does but mine has OpenWRT flashed on it so can't check)
Used as a router with another modem, its still a router.
The basic principle is the Internet is broken up into smaller subnets and a router passes IP traffic between different subnets, because they can't see each other directly but know from the routing table which gateway is connected to which subnet. Without that there would be no way to know which pipe to send any given traffic down to reach its destination.
In a home router case its relatively dumb about it, assuming that our ISP router is the right place to send any packet not destined for a private IP address. (which wouldn't usually reach the router anyway as the switch would send that direct on the LAN side)
A bridge doesn't care what protocol is in use as its working at a lower layer, it merely passes packets from one network adapter (or port if its a switch, but same thing) to another, virtual or otherwise.
A bridge and a switch are functionally the same thing, except a bridge may actually be translating the data from a tunnel inside another protocol (DSL,GPON, etc) and converting it back into standard ethernet. Which is why you can connect a computer directly to a modem and have it get the public IP address, but you need a router to perform NAT in order to translate between multiple machines with private address and that single public address. For all intents and purposes, the Internet only sees ONE device connected, the router, it has no clue how many devices are on the other side. Its slightly different once you have multiple public IP addresses but there must be thousands of guides out there already that can explain that better than I can.
Plus there's the whole IPv6 where technically you could bypass having a router at all, depending on how the ISP is configured, if you didn't care about security. Because the ISP router already knows what subnet is on your side of the link and it will broadcast back to your network what gateway it needs to talk to in order to reach the other subnets.
I hope I've not confused you too much, my explanation was a bit all over the place. This is why I never wanted to be a teacher.