My understanding from what research I've done on the topic is that Etype is formed through ones early years and once set remains as a sort of root. We can intigrate or disintigrate from our main type or our wing type (tho that is less common) and when healthy experience aspects of the other types through integration/growth over time, but no matter how much we develop, our core Etype will be what we first became. It is also my understanding that the Enneagram is less a tool for typing than it is for self analysis and personal growth and development.
MBTI on the other hand is what we are born as, and even if we develop to become somethign that appears to be vastly different from our rtue type, our natural born preferences will still be there exerting a subconscious pull and influencing us in subtle ways.
As for the correlation between them, I beleive Cogdecree was working on such a project through surveys not long ago, but I don't know if anything ever came of it (I was/am looking forward to his/her findings).
From my point of view, MBTI is the core and Ennegram further shapes that core in irrevocable ways, but it is the environment of youth what is the doing the shaping. Theoretically, any MBTI type can be any Etype, but some will be more common and others virtually non existant, but the EType when combines with MBTI helps explain some of the differences between people of the same MBTI type and might also explain why some of us have a harder time pinpointing both our true MBTI type and our core Etype (I'm still uncertain of my Etype and trying to work through several possibilities as I research it furhter)