I think the rules to shuffle chess have not been set in stone, but...usually, it's required that the players get one dark squared B and one light squared one. And castling is either not allowed or allowed only when the K and R are on the traditional starting squares.
Chess 960 is shuffle chess that allows castling regardless of the starting position and requires the K to be somewhere between the Rs.
There are 960 starting positions in chess 960 (no kidding!), and 2880/2 = 1440 starting positions in shuffle chess (I divided by 2 because half of the positions are mirror images of the other half).
Adding the 960 castling rules to shuffle chess would result in chess 2880, because there would then be no mirror images. See here.
I am safe to say that the main difference between Shuffle chess and Fischer Random (Chess 960) is that with Shuffle Chess there is no castling and the bishops can start on the same colour depending on the drawing order of the pieces?