Eh, kinda. The .30 Luger is bottle-necked and the Super is tapered. Ballistically the same though. The Super is just a tad smaller overall, and I'm sure S&W and Federal needed the smaller cartridge to fit the existing pistol for greater capacity. I wouldn't be surprised to find that they used the Luger as inspiration.
Don't know if it's correct but according to Wikipedia the .30 Pederson cartridge ( for a conversion device intended to make 1903 Springfields into lower powered blowback semi-autos) was may have been the grand pappy of the idea:
"The US .30 Pedersen cartridge (auto pistol ball cartridge caliber .30 Model of 1918 or .30-18 Automatic) used in the Pedersen device was the basis for the 7.65×20mm Long. The cartridge dimensions were identical, although Pedersen device cartridges were loaded with a slightly heavier 80 grains (5.2 g) bullet which achieved a velocity of 1,300 feet per second (400 m/s) in the longer barrel of M1903 Springfield rifles."
https://en.wikipedia.org/wiki/7.65×20mm_Long