Broadband and ADSL are quite different - quite confusing because of the way they are both marketed.
For example - in the UK BT offer 'Broadband' - it is ADSL, very old technology which has been around for years. Very smart that it uses the 'spare' capacity of a pair of copper wires.
However, there are limitations - the download speed is the 512K/1M you are quoted, but the upload speed is significantly less. Hence the term ADSL - A - Asymetric.
The cable companies have a different infrastructure. It's cable therefore you get true Broadband. I.e. the download/upload speeds are the same. It's on a dedicated piece of wire.