I wrote this on WSS and thought it would be good to share here as well.
I think extrovert and introvert in socionics are more Jungian than Eysenck or Big 5. Socionics E/I imo deal with attitudes and in Eysenck/Big 5 the concept of attitude is lost. Extroverted attitudes towards the external world and treating it as objects and introverted attitudes towards the self are the primary concepts in Jung and imo socionics typology. Althrough Aushra uses Object and Field as her concept of I/E I think going into philosophy and cognitive science there are better terms. Extroverted attitudes attempts to present external reality at different levels of reference and self-reference vs introverted attitude and it's also my opinion that some functions produce aggregate information which is referential to some other information. In this way some information may be distant from external reality by way of significant computational processes. Intuition has been studied to be a sort of sensory aggregate, not rationally conscious but still connected to sensory information. So in this way intuition references sensing, but this does not mean it necessarily is a self-reference as a sense of self is not necessary for this computation. Extroverted intuition is simply a attitude away from self reference that references sense information. Extroverted sensing would be a attitude away from self-reference that represents sense information. The introverted attitudes contain a self-referential component and it is this self-referential component that characterizes the introverted attitude. The reason that extroverted intuitive might be characterized as introverted extroverts is because the mechanism of extroverted intuition is distanced from direct sensory representation, and occurs in the mind. In summation, E/I are attitudes towards self-reference. I think in socionics there is another layer of possible references within the model which is Internal and External. Internal information elements and external information elements have a level of referential distance vs "sense reality", internal elements being N/F are distant and in a way aggregate content while S/T external elements attempt to present things as is.