Difference between repeated poles and distinct poles?
Repeated poles simply means there are more than one pole at the same location. If a pole is not repeated then it is a Distinct Pole. Consider the simple case of a cascade of two integrators (in s) which is similar to the cascade of two accumulators (in z).

The Laplace transform of an integrator
Is $\frac{1}{s}$, which is one pole at the origin. Two integrators in cascade would be $\frac{1}{s^2}$ so has repeated poles at the origin. The same with two accumulators in cascade would be $\frac{1}{(1-z^{-1})^2}$, which has repeated poles at z=1.

If there were two poles at z=1 and a third pole at z= 0.5, then such a system would have two distinct poles.