What this means is, that ever single one of the following
Jack Be Nimble (who jumped over burning candles for fun)
Jack the Giant Killer (who sold his cows for magic beans then robbed and killed a giant)
Stingy Jack (who tricked the devil so many times he was banned from both afterlives)
Jack of Jack and Jill (who splattered his head open falling down a hill)
Jack o’ Lantern (the headless horseman spirit of halloween)
Jack Frost (the spirit who heralds the end of autumn and the start of winter)
Are literally the same jackass who made so many bad life choices he ended up an immortal ice dullahan with a pumpkin serving as both his head and flashlight
but what an incredible journey he had getting there
He’s Ye Olde Florida Man
The Jack from the Fables comics is this. He is The Jack and all the same Jacks (same with Prince Charming).
Why does everyone mistake Jack and the Beanstalk with Jack the Giant Killer?
(Deep breath)
OK, now, Jack and the Beanstalk is the one with the magic beans and the one giant.
Jack the Giant Killer is about a clever boy named Jack who with cunning manages to kill eight or nine different giants and a wizard, about all through straight up trickery. For his deeds, he became a knight of the Round Table.
The second is less well known, but they are definitely two different stories. You could have overly-trustful Jack of the Beanstalk story transition into the cunning Jack of the Giant Killer story who taunts giants into pits then strikes their head with a pickaxe among other such deaths, but please stop mixing the two.
(Which isn’t to say that every every-man in English is “Jack”; sometimes it’s Tom, or Dick, or Harry, or Johnny, or what have you.)
No, not all Jacks are “the same guy”. (But all Jacks are meant, on some level, to be relatable to the consumer of the story.)
Please for the love of god don’t ascribe this theory to “folklorists”. No folklorist who knows anything about folklore is going to subscribe to this theory. (And, as previously pointed out – the link in the original post here just goes to a Wikipedia page about the Jack Tales, which does not, in fact, say anything about this theory, let alone provide documentation that supports it.)
It’s a fun idea used in some works, like “Fables”. That’s all it is. (And that’s enough! It’s fun. But it’s not “better” or “more authentic” or anything like that.)
Vengence is Key 