With S1 data, I realise that the intensity band is the square of the amplitude band, but what is the practical difference, i.e. why is the intensity band provided, and what should I use when e.g. making a difference image?
Amplitude is what is measured by the sensor, stored as 16 bit integer.
In order to keep the file size small (for reasons of downloading and transferring data) you usually convert it to intensity (32 bit float) by yourself.