Just in case it's news to anyone, if you Google "cognitive extraversion," you get a grand total of
82 hits — many of them from internet forum posts like the ones in this thread. The idea that MBTI E/I — and/or Jungian E/I — is just about "where you get your energy" (or something) and that "social" E/I is something different is mostly an internet forum meme, rather than something you'll find in Jung, Myers or other reasonably well-known MBTI-related sources.
Jung certainly didn't talk about two different kinds of extraversion, and anyone who thinks Jung didn't strongly associate extraversion and sociability/interaction either hasn't read
Psychological Types or didn't drink enough coffee while they were reading. Jung spent more of
Psychological Types talking about the things he thought
all extraverts and
all introverts tend to have in common than he spent talking about all eight of the functions put together — and, as far as Jung was concerned, if your dominant function had an extraverted attitude, that meant, by definition, that you were a Jungian extravert.
Here's a little bit of what Jung had to say about extraverts and introverts:
Jung said:
[Extraverts and introverts] are so different and present such a striking contrast that their existence becomes quite obvious even to the layman once it has been pointed out. Everyone knows those reserved, inscrutable, rather shy people who form the strongest possible contrast to the open, sociable, jovial, or at least friendly and approachable characters who are on good terms with everybody, or quarrel with everybody, but always relate to them in some way and in turn are affected by them.
Jung said:
Extraversion is characterized by ... a need to join in and get "with it," ... the cultivation of friends and acquaintances, none too carefully selected, and finally by the great importance attached to the figure one cuts, and hence by a strong tendency to make a show of oneself.
Myers and Briggs, in turning Jung's theory into the MBTI typology, viewed E/I much as Jung did — multifaceted, including various elements normally associated with sociability. And whether you're looking at MBTI sources that focus primarily on the four dichotomies (and combinations thereof) or MBTI sources more focused on the "cognitive functions," sociability is virtually always included in the E/I mix. Four of the entries on Kroeger & Thuesen's summary 10-word list of extraverted characteristics are "sociability," "interaction," "multiple relationships" and "gregarious." Keirsey's type test includes E/I questions like "Do you think of yourself as (a) an outgoing person or (b) a private person?" and "At work do you tend to (a) be sociable with your colleagues or (b) keep more to yourself?" Lenore Thomson says extraverts are "outgoing, sometimes highly expressive," and "are influenced and gauge their worth by the expectations and attention of others."
The MBTI Manual is full of charts showing the results of various studies that have found statistically significant correlations between the MBTI dimensions and other personality measurements. MBTI extraversion correlates positively with traits like "affiliation," "sociability," "social presence," "exhibition," "gregariousness," "expressed affection," "talkativeness," etc. MBTI introversion correlates positively with traits like "controlled," "social introversion," "reserved," "shy," "defendance" and "infavoidance" (avoidance of embarrassment).
It's also worth noting, though, that Jung said he thought more people were in the middle on E/I than were significantly extraverted or introverted. So Jung certainly believed in ambiverts, but I'd say it's pretty clear that he thought an ambivert was someone who lacked a well-differentiated dominant function — so that, e.g., a person couldn't simultaneously have an extraverted dominant function and be a Jungian ambivert. If you look at the way Chapter 10 of
Psychological Types is organized, Se-doms, Ne-doms, Te-doms and Fe-doms are presented as the four types of extraverts and Si-doms, Ni-doms, Ti-doms and Fi-doms are presented as the four types of introverts.
Like the most popular version of the Big Five (the NEO-PI), the Step II version of the MBTI breaks each of the dichotomies into multiple facets, with the idea that it may be possible to be, e.g., an overall extravert but score "out of preference" (i.e., introverted) on one or more of the E/I facets. And, as noted above, the MBTI dimensions have
always been "multifaceted" in the sense that each preference involves what psychologists often refer to as a "cluster" of personality characteristics that tend to co-vary to a statistically significant degree. But, just as all biological males aren't sexually attracted to females, there's never really been any reason to expect that, for any given individual with a particular MBTI preference, they'll necessarily exhibit
all the characteristics that tend to be associated with that preference.
So I'm not saying that any given extravert's social inclinations and/or behavior might not be more consistent with the introvert cluster than the extravert cluster — but there's every reason to think that that's true of most of the characteristics associated with all four of the MBTI preferences. So I'd question whether it really makes sense to talk in terms of "two kinds of extraversion" — and in any case, to reiterate my opening point, the concepts of "cognitive extraversion" vs. "social extraversion" aren't really consistent with Jung or Myers, and barely exist outside of internet forums.
