If we discretize our plant with the ZOH method then its output will be step-like

The theoretical and the ZOH discretization methods map the continuous into the discrete poles according to the theoretical definition

Differential equations are more general than difference equations

The variable s appears in Laplace transforms and the constant T (sampling period) can also appear

The main difference between digital and analog systems is discrete or continuous

time

Systems of relative order zero in discrete time are strictly causal

The basic operation in continuous time is integration, in discrete time it is a 1-period time delay

The variable s appears in Laplace transforms and the variable k (number of periods) can also appear

The discrete root locus rules branches are different from the continuous ones because they would repeat periodically

The variable z appears in discrete (Z) transforms and the constant T (sampling period) can also appear