No, the stars are not completely arbitrary.
Admins have 5 gold stars.
Moderators have 4(?) blue stars.
For those who have a status of "member," the number of stars you have depends on how many posts you have made.
For those with a status of "friend" or "friends," I believe they have two stars, which does not change.
I could fairly easily change this, as it would just require a few minutes tinkering with the forum settings, but I figure why bother.