We don't have Shonen Jump here, we do have manga compilations. You see, a manga series is released first in a manga series magazine like Shonen Jump, and then it's released in an "album" version, with about 8 chapters in each book. We have those here.

The japanese Shonen Jump is where the new manga series get published, it's very ahrd to get your own manga series published on Shonen Jump. The most popular ones are turned into anime, some are not.

The american Shonen Jump, from what you've said, is merely a collection of popular manga, not exactly the "translated" version of the original Shonen Jump.