Yes, the Student Advantage card nets one 15% off, but the ISIC card does not. You have to join the Student Advantage program to get the discount.
Alan, that's not correct. As a former student, I used my ISIC card many, many times to get the 15% discount on Amtrak. I just went to Amtrak.com to double-check, and sure enough, when you make your reservation, one of the options for "passenger type" is "ISIC", which nets you a 15% discount.
Incidentally, I was never, ever asked to produce an ISIC card or a student ID, and I used the ISIC discount dozens of times. Even after my card expired, Amtrak.com would still accept the number. I stopped using it after I was no longer a student, though.