An ISDN modem is typically a device that hooks into your PC's serial port. You can then use it just like an analog modem and configure a DUN profile. If you have an ISDN router, then you have more options. The PPP is done from the router and is transparent to your PC, which is connected to the router via ethernet. ISDN routers and ISDN modems give you the same bandwidth, up to 128Kbps, but the ISDN modem introduces quite a bit of latency. An ISDN router gives you about 30msec latency to the NAS your are dialing into, while an ISDN modem would run closer to 100msec.
As for newbie's question, I think they call it a modem because the client's OS uses it like a traditional modem. But you are correct in questioning the terminology, since there is no modulation/demodulation from analog to digital.
Forcesho's response is correct in that some routers allow you to utilize the ISDN port as a virtual modem that the client PC can attach to over the network, but these routers are usually more expensive. He's a good guy so if you want to buy his ISDN modem, I'm sure it will be a good piece of equipment. I used to have a Motorola Bitsurfer Pro back in the day -- boy was I glad to get rid of it and get a router!