I wonder how one reconciles the differences between Exodus 20:1-17 and Deuteronomy 5:6-21. Also, Exodus 34:12-26 seems to be referred to as The Ten Words/Things (Commandments). So, what is the traditional understanding of which words appeared on the stone tablets brought down from Mt. Sinai by Moshe?

Some commentaries understand that the passages of the Aseret Hadibrot in Devarim (Deut.) were written on the second set of tablets. Others understand that they are a commentary on and an expansion of the first. There are all told 16 differences between the two. Many understand that the second set was directed specifically to the Jews (Bnei Yisroel) after they had agreed to accepting Torah, whereas the first set were the ones offered to all the nations of the earth, as per the Midrash. This last interpretation is true regardless of which (or a potential third) explanation one gives for what role the second version accomplishes. There are several internal allusions to this latter interpretation.