There is the original J31
Then they produced a J32 which has 1050SHP engines and slightly better engineering features, like you don't need to empty the tanks to change a fuel pump. And it also has automatic cooler flaps.
There is also the EDAM option which is for better performance. It looks like 2 wedges either side of the engines.
Type rating is valid for both. And there is no currency issues swapping between them.
MJ