Why do we use discrete-time sampling?
There is a difference between a quantized signal, i.e. taking only integer values, and a sampled signal, i.e. the value of which is only looked at on spaced instants.

A physical signal is usually continuous in values and in time.

An A/D converter turns a physical signal in a quantized one; if the converter is asynchronous, it generates a time-continuous signal.

Discrete-time/continuous-value signals are created by sample &amp; hold circuits.

And digital signals processed by computers are usually both quantized and time-discrete.