As nouns the difference between stats and metric
is that
stats is (informal|in the singular) a short form of
statistics (
the subject ) while
metric is a measure for something; a means of deriving a quantitative measurement or approximation for otherwise qualitative phenomena (especially used in software engineering).
As an adjective metric is
of or relating to the metric system of measurement.
As a verb metric is
to measure or analyse statistical data concerning the quality or effectiveness of a process.