Relation between uncertainty in measurement of mean and standard error on the mean

I have a series of individual (time) measurements with a certain uncertainty each per measurement, which is the same for all the measurements (±one frame). I have understood that the uncertainty on the arithmetic mean of these measurements will be equal to that same uncertainty of the measurements (±one frame in this case). I am completely lost on how this relates to the standard error from the mean (I suspect the standard error is an additional error on top on the uncertainty that comes from the underlying parent distribution and true value). How would one combine the uncertainty in the mean from measurement with the standard error, to give a "final" error (±) for the mean?