Suppose that for some reason the first group of test takers were mostly average and the second group of test takers were mostly geniuses. If the test makers scored the test based on the performance on each seating of the test then someone who is slightly above average in the first group will get a "high" score and someone who is slightly below genius in the second group will get a "low" score. That wouldn't be fair. Hence the test needs to be scored in some absolute manner. There are statistical techniques for achieving this.
The answer to the original question is that for SAT tests that are reused, the curve is the same as when the test was first administered. Same test means same test difficulty which means the same scaling curve.
Unfortunately Fignewton is wrong. The experimental sections matter as well. Additionally, the experimental sections vary each time, even though the test is still the same. Even though this is a late post, the info is still relevant. While it is partially true that the difficulty is assigned prior to the test, it is also true that the EXPERIMENTAL SECTIONS FOR THAT TESTING DATE ALSO MATTER IN THE EQUATING PROCESS
See the link: What happens between when you finish the SAT and scores come out? - The SATHabit Blog
Repeated tests have the same experimental sections and the same curves. As has been explained above, a student's score is not affected by the performance of others taking the test on the same day. See here: