The SS package came with spinner hubcaps, engine turned side trim inserts, a grab bar, an "Impala SS" emblem on the rear trunk lid, SS emblems on the rear quarters, engine turned rear coves and rear panel (some earlier SSs had flat aluminum), buckets seats, and a console between those seats.
I might have missed a few things, but others might chime in. Basically the SS option was a "trim package". The engine and transmission options were the same for both cars. Originally this total package cost something like $121.25 from the factory. Here is a picture of my original invoice: http://web.missouri.edu/~kochtanekt/www/1962ImpalaSS/1962invoice.jpg