Simplified, classically, it goes something like this:
- Modems (modulator/demodulator pairs) are used to communicate over >1 modes of PHY, without participating in LNK.
VT102 - modem - POTS - modem - VAX
host - [ modems] - host
- Bridges are used to communicate over >1 modes of LNK, without participating in NET.
computer - ethernet - cable modem - DOCSIS - CMTS - ethernet - DHCP Server
host - [etheret bridges] - host
- Routers are used to communicate over >1 modes of NET, without participating in TRN.
TV Settop Box - WiFi - SOHO gateway - FTTH - ISP gateway - CDN gateway - Netflix
host - [routers] - host
It goes up and on through the layers, but there are few practical examples of simple discrete modems, bridges, and routers to begin with.
Dialup modems eventually began managing link functions such as compression and flow control... The simplest commercial cable modems of the mid-90s were always bridges,though now they often run nearly the full gamut, some even capable of content filtering. Fortunately, many multi-function devices can have their higher capabilities disabled, allowing those functions to be administrated elsewhere, which seems to be the case here, as you now administrate your own routing, including NAT and QoS, instead of your ISP doing so at your 'modem'.
The OSI model has never been quite discrete in practice, though emergent technologies are usually more delineated while standards and best common practices are getting hashed out.