Mechanically, nothing, except for a model 52 4-door sedan which had a 125.5 inch wheelbase instead of the rest which had 121.5. Body styles varied as did both internal and external trim details and levels.
Depending upon what year you are talking about, they may have different engines. For example, in 1950 the Super (50) received the improved (small straight 8) engine with hydraulic lifters, while the Special (40) received the older version.
The Series 40 (Special) was always the economy Buick. It generally shared bodies with Cheverlot, Olds, and Pontiac. The Series 50 (Super) was the mid priced Buick. It featured upgrades from the Special. The Series 70 was the Roadmaster. After WW II, it was the top of the Buick line.
The 40 series had the 248 motor and the 50 series had the 263 motor for the first time in 1950. Both had hydro lifters with the dynaflow, mechanicals with a stick. You can tell with a quick look that the special (40) series has a split windsheild and the super(50) series has a one piece wrap around. The super also has 2 small wing windows in the back and the special does not. It looks like the same car but has small differences. The 263 was a very good engine but was phased out in a couple of years to make way for the new v-8 nailhead.