What is the difference between a transistor being use as a switch and as an amplifier?

When used as a switch, a transistor is usually driven completely on (saturation) or completely off (cutoff). There are a few kinds of switching circuits though (e.g. ECL) that avoid saturation/cutoff to obtain faster speed, these operate on a fixed constant current and switch it through one of two transistors.

When used as an amplifier it is biased so that it operates in a linear, or near-linear, part of its characteristic curve so that the output faithfully copies the input.