Parameters and sample statistics
Mean, standard deviation, variance etc. are all both sample statistics and parameters, depending on the circumstance of their use, which are:
Measures of a population
If one had the necessary information about all the individuals in a population, one could calculate any descriptive parameter, like their average height. These are population parameters.
Measures of a probability distribution
Probability distributions have parameters that describe certain characteristics about the distribution, like its mean.
Measures of an uncertainty distribution
Confidence distributions have parameters that describe certain characteristics about the distribution, like its mean.
Measures of a sample
One can calculate some statistics for any set of values, like their mean. If that set of values is drawn at random from a population or probability distribution, the statistic can be used to estimate the population or probability distribution parameters (the sample mean can be used as an estimate of the corresponding population mean, or probability distribution mean, for example).
Monte Carlo simulation results
The results of a Monte Carlo simulation are effectively samples from the output probability distribution the simulation is trying to determine.
There are therefore five situations in which you will come across terms like mean, standard deviation, percentiles, etc. In each situation they have different meanings and are defined and calculated differently. These links provide an explanation for the most common terms: