H9 and 3L55 says you have a limited slip differential with 3.55/1 ratio. Not sure which differential you have, 9 inch or 8.8, but if it has a removable cover on the back it is not a 9 inch. I believe that they gave you the right lube but you will also need to add friction additive for the limited slip. The reference to transmission type is that some manual transmissions also use this type lube.
Someone more knowledgeable may be along soon.
God Bless
Whisler
Frankenstein: 1989 F250 4X4, C-6, Hurst Pro-Matic 2 shifter, carbed '84 351W, Edelbrock manifold, Edlbrock AVS, DS2 ignition, 3G alternator, JBA shorty headers, no cats, dual exhaust with H pipe.