The Zohar says, that the thirteen middos of micha are upper level middos, and the 13 from Moshe are the lower of those middos. The Gr"a explains, that the upper middos are the "inner" ones, and the lower ones are the "outer" middos.
I have seen this explained - in the footnote of the attached sefer - as follows:
If you go to a country and see the people interacting with each other [kind or mean], you will assume that the leader of the country acts that way. When people act with mercy, you can tell the ruler acts with mercy, and so on. The upper level middos, are the ones that Hashem himself uses "inside", while people emulating Hashem use the lower level of those same middos "outside".
The way Hashem uses those middos - the upper middos, and how we are to use them - the lower middos, are described in detail in the first perek of the sefer Tomer Devorah.