I've got this one.
First off, great diagram. Okie dokie, he used to have web shooters. In the 616 (or regular) universe, when Peter Parker first created his Spider-Man alter ego, he invented these web shooters, and the synthetic formula for webbing, to help aid in his "Spider" act.
Then the movie decided to give him "organic" web shooters from his wrists, because it was more "believable." They said a teenager would never have been able to develop a web shooter device or a synthetic webbing formula that could do all the things it could do, with only a rudimentary chemistry set and his high school equivalent education.
In keeping with the "new readers" the movie would bring in, the comics decided to reflect more of the movie, ostensibly so the new readers wouldn't get confused. The irony is, the elaborate, continuity-heavy explanation for how Spider-Man gained his new "organic" web shooters (turned into a spider, then birthed out of it and had that one alteration in his body chemistry, short version), was much more complicated than simply saying, "Yeah, in the comics he built those."
