MoDem = Modulator - Demodulator. Required to extract the data signal from the modulating signal which is the carrier signal.
Cable carrier signals are different to ADSL phoneline carrier signals so different MoDem circuitry is required.
A cable router has no MoDem circuitry and so depends on the external NTL cable MoDem to do that job.
ADSL routers are routers combined with ADSL MoDem circuitry. However I'm not aware of any which offers the facility to switch off its integrated MoDem and simply allows a "bridge" to the NTL cable MoDem instead.