As to why the numberings are different,
this article should help.
One thing I like about the Augustinian numbering is the resulting symmetry that does not exist in other numberings. Specifically: not committing adultery and not stealing are numbered separately by all. But only the Augustinian numbering separately prohibits in thought (#9, #10) what earlier commandments (#6, #7) prohibit in deed.
Also, according to ancient tradition, numbers have significance (for example, three is the number of perfect completion for the Jews, and for Christians the number three symbolized the perfection of the Godhead—the Most Holy Trinity. Similarly, seven signifies spiritual perfection and fullness or completion – God rested on the seventh day, seven gifts of the Holy Spirit, etc.) In the Augustinian numbering, there are three commandments which cover our relationship with Him, and seven commandments which cover our relationships with our fellow humans. In the other numberings these are four and six, respectively (which strikes me as odd).