What is the difference between an automatic voltage stabilizer and an automatic step regulator?

Generally the voltage stabilizer has a very precise single fixed output voltage e.g. a laptop adapter with an output voltage of 19.8V DC
The step regulator is a more expensive device designed to handle a much wider range of input voltages compared to a simple voltage stabilizer/regulator. It can step up or down the input voltage as required as well as regulating the output voltage.
They should be equally precise in maintaining correct output voltage within their operating parameters, subject of course to their regulation specification e.g. max 0.5% variation, 0.1% etc.