I initially mistyped as an INFJ. I relied too much on the stereotypes of the P/J divide. Plus, my initial behavior when one first meets me might come off as a stereotypical J. This is probably do to my mom's personality rubbing off on me. She's been a huge part of my life, and has a rather distinct J preference. I also wasn't looking into cognitive functions.
Then I mistyped as an INFP before realizing that I'm an ENFP.
I think a lot of ENFPs can be socially introverted because Ne is really self-stimulating. Personally, I can't determine whether I am social introvert or an extrovert. I'm most likely to be social when I know I can freely express myself. Back when I thought I was a cognitive introvert, I had much more anxiety and insecurity. This led me to believe that people wouldn't accept me as I am, so I sort of repressed Ne.
Then again, Ne isn't necessarily social. I certainly have used it in social circumstances. My first semester of college, I took a course about this process called design thinking and problem solving and creativity. I really was encouraged to express my Ne there. The professor was also really good at dividing us into teams where we really balanced each other out. So, I really brought my Ne ideas to the table when brainstorming and thinking of the possibilities. That was sort of the "a-ha" moment when I realized that Ne is an asset when interacting with other people. I used to socially before then, but it was mostly used in a light-heartened way
If someone were to mistaken me for an introverted type, it would probably be an INFx. Though, as someone gets to know me, there's a higher chance that they would think of me as either an INFP or an ENFP. The jury is out on which.
One of my best friends is an INFJ. She and I have a lot in common temperament wise--we come off as positive, cheerful, sweet, slightly absent-minded people. I suppose someone could mistaken her for being a quiet, introverted ENFP at first.
It is really interesting to think about the divide between cognitive E and I and social E and I. It would be interesting to get a better sense of the numbers, but it appears to me that both match up for most people. I have met a lot of cognitive introverts though who will appear rather extroverted in some social situations. Or at least they will appear to be social. Or they just really are excited to see me and enjoy spending time with me, so maybe it's just something I see.
I hope my point makes sense, as I feel like I'm rambling a bit.