Functional
One summary of the data set beside the same summary of the fitted density.
The part of this class an input modeller is most likely to act on. A test says reject or do not reject; this says how far off the fit is on a quantity a simulation is sensitive to. A queueing model driven by these service times responds to the mean and the coefficient of variation far more than to the shape between them, so a fit that reproduces both to within a percent is adequate for that purpose whatever a goodness-of-fit test says about it.
The fitted value is computed from the distribution rather than from a sample of it, so it carries no simulation error of its own.
Parameters
what is being compared
the value computed from the observations
the value computed from the fitted density