The 38 Super is a semi-rimmed round designed for semiautomatic handguns. It started life as the 38 ACP but was upgraded (and this is probably the very first +P round, although not called that) to a more powerful and higher pressure loading. With the new load the name was changed to 38 Super.
The 38 Smith & Wesson Special was introduced right around the turn of the century. It was initially designed/intended at a black powder round but never commercially loaded that way. Its introduction was as a smokeless powder load. It came from the 38 Long (Colt) which was chosen by the US Military in 1892 to replace the black powder 45 Smith & Wesson load they had been using in their 45 Colt SAA revolvers. The 38 Long was chambered in a DA Colt revolver.
The 38 Smith & Wesson is an older cartridge (introduced in 1877) that survived into the 20th Century and the smokeless era. Its original bullet weight was 145g but there were several loadings with 200g bullets, one of which became a British service cartridge (called the .380/200). The 38 S&W has a larger rim, base and bullet (.359-.360") than the 38 Special. They can sometimes be forced into 38 Special chambers and fired, causing the uninformed to think they are interchangable. They are not.
Hope this explains a little.