I have had 3 of the molded Fender cases over the past several months. I bought them used, so I don't know exactly which model they are - if they're the basic generic P/J case or were matched with a specific bass or model. They all looked pretty much the same.
I also have a '62 RI Jazz and '62 RI P.
Two of the cases fit both basses, and one of the cases fit just one of the basses (I think it was the P that fit, but I sold that case and don't remember for sure). Also, on the cases that fit both the P & J, my Stingrays fit in there as well. A stingray should fit in the same case as a P.