The phrase "Ten Commandments" generally refers to the very similar passages in Exodus 20:2?17 and Deuteronomy 5:6?21. Some distinguish between this "Ethical Decalogue" and a series of ten commandments in Exodus 34 that are labelled the "Ritual Decalogue."
The phrase 'aseret had'varim' is only used in reference to the 10 commandments in the first tablets, not in the second set, not that they were/are not followed, but they in no way override the previous commandments. For a proper translation of the ten commandments and the rest of the Torah I recommend using http://bible.ort.org/books/pentd2.asp which I helped put online.
We could go into a full scale debate about the authorship of the five books of Moses, but I shall refrain from that given the hour.