Saying "38" is not enough. There's a bunch of 38s. Off the top of my head I can list 38 S&W, .38 Special, 38 Largo, 38 Colt, 38 New Police, 38 ACP (Auto Colt Pistol), 38 Long, 38 Short, 38 Super, 38-200, 38 British. Some ar actually the same with differing names. That's just the ones I can think of, there are many more.
In America most people think of the 38 Special as THE 38.
The 9mm (.355) is almost the same bore diameter as the 38s (which actually run .357-.363). The 9mm Short or Corto (380 ACP in America), 9mm Largo, 9mm Baynard, 9mm Bergmann, 9mm Luger (also known as 9mm Nato, 9mm Parabellum and 9x19), 9x23 and some I don't recall.
To answer your question, the 38 Super is a semi-rimmed auto cartridge intended for the Colt 1911 platform that originally used a 130 FMC (full metal case) at nearly 1300 FPS. This load has great penetration and if I knew my opponent would be wearing a vest this is the handgun I would want. Recent factory loads for the caliber are greatly reduced out of liability fears. Now Super ammo runs the same speed as the old 38 ACP. Must load your own for full performance.
The 38 Special is a revolver cartridge that can generate 900-1200 FPS with a 125 grain bullet so when loaded to its full 1200 FPS potential (most factory ammo is way below full potential) it competes with the Super in performance.