\( \mu x\) is a force of mortality. It is a rate.
\(mx \) is a weighted average of this force, weighted by population. If the size of the population is larger, \( \mu x\) has a larger population on which to act. As the population decreases from the resulting deaths, \( \mu x\) has a smaller population on which to act.
These two measure are equivalent if \( \mu x\) is constant for age label \(x \). In the estimation procedure, this is assumed and as such the estimations are the same.