it neither modulates nor demodulates so I won't call it a modem.
'Course it does Malcolm! It's just that there is usually an Ethernet router (and a WiFi access point) built into the same box. "Modem" is frequently taken to imply a dial-up connection, but the term is no less accurately applied to the ADSL line interface.
Modulation is the process of converting the plain signal (in this case the TCP/IP packets) into another form for transmission through the desired medium (POTS phone wires), demodulation is the recovery of the payload from the received signal (which could be substantially modified from that transmitted by the characteristics of the medium). Another example: FM radio - the audio waveform is used to vary the frequency of a VHF oscillator, and the resulting RF is launched into the ether by a properly designed antenna. At the receiving end the variations in frequency are demodulated back to a facsimile of the original audio.
ADSL is an extremely sophisticated modulation scheme which adapts to the specific line characteristics between the transmitter and receiver, and does not simply send serial data as individual bits or even as an encoded (for error compensation) bit stream. The data encoding has similarities with the methods used to achieve high data densities on hard drives (think of the disk platter as the transmission medium), although the modulation is different to account for the differences in the physical medium.
To go into a bit more detail, the available frequency band (from about 150kHz to 1100kHz) is divided into 4kHz channels, each channel is tested for the data rate it will support (limited by the transmission characteristics and interference on that channel), then the data stream is divided up across the channels accordingly, encoded, and multi-bit symbols modulated onto carrier frequencies using amplitude and phase shift, and pre-emphasised to overcome distortion in the transmission line. At the receiving end each carrier is demodulated, decoded, error corrected, and then the bit streams from all the carriers are combined to recreate the original bit stream (and then used to recreate the TCP/IP packets). In effect, the data is being spread over 250 channels instead of just one.
The upload channel is much slower, using many fewer channels between about 25kHz and 150kHz. That's why it's called "Asymetric".