They are no more separate than two different interpretations of the Enneagram. Both are rooted in the work of Jung, and each uses a four-letter code to identify the 16 subtypes originally described by Jung. There is some variation in the code used, but they identify exactly the same 16 Jungian subtypes. Therefore, there is a one-to-one match between MBTI types and Socionics types. There may be differences in MBTI results and Socionics test results, but these are only differences in test results. There is a difference between your true type, which is what the tests are trying to determine, and what type you test as. Although there are some differences in the systems, these seem to be complementary differences of focus, not fundamental contradictions. As far as I can tell, Socionics is no more different from MBTI than Keirsey's system is. MBTI, Keirsey, and Socionics are all elaborating on the original work of Jung, and they should be understood as complementary, not as fundamentally different systems.
They're all based on the work of Jung, but they all have radically different methodologies, which makes them separate, even if they are indeed closely related. Socionics is very different from MBTI, for a few reasons, including:
Socionics' interpretation of Jung's functions is actually very slightly different from the functions as originally described by Jung, because while Jung's functions were originally described as symbols for different styles of thought, Socionics functions (which Socionics itself calls "Information Metabolism" elements), are more concerned with how an individual interacts with his environment. This is most apparent when comparing Fi/Fe as it is used in the two systems: In MBTI, Fi and Fe are two different ways to manage ethical values (Fi users make choices on basis on a personal set of ethical or aesthetic, etc. values whereas Fe users make choices based on societally-held values -- what other people think is right); whereas in Socionics Fi and Fe refer more to a person's focus on interpersonal relationships. Socionics Fi valuers like making very deep and committed emotional connections with a few people, whereas Fe valuers prefer to focus on a cheerful, easygoing pace of things -- which is why socionics buffs sometimes refer to enjoying "an Fe atmosphere," for example. Many MBTI Fi users greatly value Socionics Fe relationships, and often identify more with Alpha Quadra (or Beta Quadra for that matter) than Delta Quadra.
Socionics is further separated from MBTI by its inclusion of Freudian theories on the conscious and unconscious (ego, super-ego, id, and super-id especially). Socionics integrates Freudian conscience categories by dividing Jungian functions into "blocks," and thus separating perception-judgment processes by both skill of use and preference, and thus assigning them a role. Functions are classified as strong and valued (ego), weak and valued (super-id), strong but unvalued (id), and weak and unvalued (super-ego).
And then of course there's the most obvious difference: The J/P switch. In socionics, Perception versus Judgment is interpreted as the Peceiving or Judging function being the base (dominant) function, rather than it being the extroverted function, so the dominant and auxiliary are switched for introverts: Ni-Te is INTJ and INTp for example. In some correlations this tends not to matter because the functions are different enough that they still directly correlate (ISTP and ISTJ for example -- Socionics Si is closest to MBTI Se and Socionics Se is closest to MBTI Te), but in some cases the switch is crucial -- INTPs are very rarely INTp.
It's also funny you should mention Keirsey being as equivalent to MBTI as Socionics, because, erm... it actually is
(that is to say, Keirsey isn't exactly equivalent either). While Socionics loses equivalence to MBTI by being a more complex personality inventory, Keirsey does by being much shallower in its analysis. It eschews the functions completely and assigns role variants based on expressed behavior which is supposedly correlated to the functions -- and while oftentimes expressed behavior
does equate to Jungian types, it doesn't always -- ENTJ Administrators and ISFP Healers in particular are quite commonplace. Some P types with more J-ish Enneagram motivations often end up with Judgment-based role variants: Our very own Magic Poriferan, for example, (1w9 sx/sp) is likely an INTP Inspector.
So in conclusion, yes, all those systems are based on Jung's ideas, but that does not mean they are the same. In the end they are all personality inventories, and inherently limited by virtue of precisely that. Thus, the only way for one to align to one single type in all Jung-based typology systems is for one to fit every single trait ascribed to that type. Basically, to be a walking stereotype of that type.
As for treating the different types as "complementary" to Jung's original work, that's actually a bad idea, because it works under the very common and very retarded assumption that Jungian types are a naturally occurring phenomenon. All Jungian types are are personality inventories: sets of traits that the common person is presumed to fall under. Each interpretation of that system adds traits or subtracts traits from the previous, which means that since the majority of people don't fit perfectly into one type, different traits from different types working on the same basic framework could fit one single person. The same could be said of different interpretations of Enneagram: If they are different enough they might as well be different systems based on each other.
