The Ghostbusters II game we got in America, developed by Kemco and published by Activision, was poop. Meanwhile, Japan and Europe got a completely different Ghostbusters II game called New Ghostbusters II by talented developer HAL Laboratory -- creators of Kirby and Lolo, and employer of future Nintendo president Satoru Iwata. It was much less poop-like.
New Ghostbusters II never came out in North America, likely because Activision had already secured the rights for a game based on the movie. Nintendo Player discovered (and dumped) a prototype of an unreleased US version of HAL's Ghostbusters II game, and documented the minimal differences between that version and the ones released elsewhere.
Apparently, HAL did have plans to release this at some point! And then, for some reason, potentially because of interference from Activision or Vigo the Carpathian, it instead became the footnote it is now.