You are right. I cannot just say because they "share" the same functions, they are the equal. However, I have found the functions to be identical. They may use different wording but the same meaning. And yes, Socionics and mbti have different systems... I just like to let others know, they can use a connection. (Also, I did study, lol... or else I wouldn't have given my opinion, in short)
Definitions...
MBTI,
Se: Acts on concrete data from here and now. Trusts the present, then lets it go.
vs
Socionics,
Se: Extroverted, irrational, and static information element. It is also called Se, F, volitional sensing, or black sensing. Se includes the ability to attain high level of awareness of the physical aspects of one's reality, to know how much physical force or power is latent or required, to be able to accurately estimate properties of material sort. Types that strongly value Se are much more comfortable taking concrete actions to change their physical surroundings. This may at times be perceived as disruptive and abrasive, particularly by Ne-types who feel that abrupt changes in their physical surrounding ruins their balance. In Se-quadras, interaction takes a more blunt and direct forms, resulting in a much strongly impacting physical atmosphere than Si-valuing types prefer. Se-types enjoy discussing possibilities but only if there is concrete gain from it, or it holds the potential to impact the "the real world". Unlike Si, which is about one's subjective sensory experience (how intense or enjoyable it is), Se is about achieving an object of desire. It gives one the ability to influence, bend, and push concrete situations and people in order to achieve such an object, rather than to subjectively assess the situation one is in.
MBTI,
Si: Compares present facts and experiences to past experience. Trusts the past. Stores sensory data for future use.
vs
Socionics,
Si: Irrational, introverted, and dynamic information element. It is also referred to as Si, S, experiential sensing, or white sensing. Si is associated with the ability to internalize sensations and to experience them in full detail. Si focuses on tangible, direct (external) connections (introverted) between processes (dynamic) happening in one time, i.e. the physical, sensual experience of interactions between objects. This leads to an awareness of internal tangible physical states and how various physical fluctuations or substances are directly transferred between objects, such as motion, temperature, or dirtiness. The awareness of these tangible physical processes consequently leads to an awareness of health, or an optimum balance with one's environment. The individual physical reaction to concrete surroundings is main way we perceive and define aesthetics, comfort, convenience, and pleasure.
MBTI,
Ne: Sees possibilities in the external world. Trusts flashes from the unconscious, which can then be shared with others.
vs
Socionics,
Ne: Extroverted, irrational, and static information element. It is also called Ne, I, intuition of possibilities, or black intuition.
Ne is generally associated with the ability to see various potentialities and possibilities, create new opportunities and new beginnings, recognize visible potential in others, be aware of different perspectives and viewpoints, rapidly generate associations and draw parallels, and be led by one's intellectual curiosity and stimulate this curiosity in others.
Types that value Ne invest most of their time into discussing various points of view, broad spectrum attitudes, trends, and phenomena, further potential and options some of which may not have happened in actuality, thereby opening up new doors and adding in new tangents to a conversation. They perceive and voice multiple variations and alternative view points, try to mediate between them, and enjoy a lively discussion that would help them settle their uncertainties and provide some grounding. Typical Ne humor juxtaposes and blends seemingly unrelated aspects with elements of unconverntionality and even absurdism.
MBTI,
Ni: Looks at consistency of ideas and thoughts with an internal framework. Trusts flashes from the unconscious, which may be hard for others to understand.
vs
Socionics,
Ni: Introverted, irrational, and dynamic information element. It is also called Ni, T, temporal intuition, or white intuition. Ni is generally associated with the ability to recognize the unfolding of processes over time (how one event leads to another), have visions of the past and future, over-reliance on mental imagery, seeing intangible hints of trends and relationships between processes or objects. Types that value Ni always like to have in mind a specific plan for how things will develop in the future which is usually based on past trends that they deem likely to recur. To assess these trends they seek to gather information of what's has taken place and transverse the time axis backwards and forwards. Thus, they often devote little time for living "in the now" or "making the best of the present". They generally engage in pure leisure activities only for short periods of time, and even then their leisure activities generally involve mentally and psychologically demanding or competitive aspect.
MBTI,
Te: Seeks logic and consistency in the outside world. Concern for external laws and rules.
vs
Socionics,
Te: Extroverted logic is an rational, extroverted, and dynamic IM element. It is also referred to as Te, P, algorithmic logic, practical logic, or black logic (because the symbol is black). Extroverted logic deals with the external activity of objects, i.e the how, what and where of events, activity or work, behaviour, algorithms, movement, and actions. The how, what and where of events would be the external activity of events, activity or work would be the external activity of a machine or individual(s) and algorithms describe the external activity of objects.
Since Te perceives objective, factual information outside the subject (external activity) and analyzes the rationale and functionality of what is happening or being done or said. "Quality" to a Te type is how well an object performs the functions for which it was made. A Te type can judge a person to be "effective" if he is able to achieve his purposes without wasting any energy or producing unwanted side effects. So Te types basically evaluate people and things using the same criteria.
MBTI,
Ti: Seeks internal consistency and logic of ideas. Trusts his or her internal framework, which may be difficult to explain to others.
vs
Socionics,
Ti: Introverted logic is an introverted, rational, and static information element. It is also called Ti, L, structural logic, or white logic.
Ti is generally associated with the ability to recognize logical consistency and correctness, generate and apply classifications and systems, organize systematic and conceptual understanding, see logical connections between things (including logical similarities, differences, and correlations) by means of instinctive feelings of validity, symmetry, and even beauty. It is like common sense, in that it builds on one's expectations of reality, through a somewhat personal, though explicable, understanding of general truths and how they are manifested.
Types that value Ti naturally question the consistency of beliefs that are taken for granted in everyday life. They strongly prefer to make decisions based on their own experience and judgement, as opposed to relying on external authorities for knowledge, which they use only as a last resort. They also have respect for people with clearly defined and internally consistent opinions, believing that a sense of internal certainty is necessary for orienting oneself in life. To these types, one's personal standards of truth are more reliable than public consensus.
They see overly pragmatic views as shallow, and try to limit public discussion of mundane practical matters. They are especially sensitive to redundant information.
MBTI,
Fe: Seeks harmony with and between people in the outside world. Interpersonal and cultural values are important.
vs
Socionics,
Fe: Extroverted ethics is an extroverted, rational, and dynamic information element. It is also called Fe, E, the ethics of emotions, or black ethics. Fe is generally associated with the ability to recognize and convey (i.e. make others experience) passions, moods, and emotional states, generate excitement, liveliness, and feelings, get emotionally involved in activities and emotionally involve others, recognize and describe emotional interaction between people and groups, and build a sense of community and emotional unity.
Types that value Fe like creating a visible atmosphere of camaraderie with other people. They enjoy a loose atmosphere where anything goes, where people don't have to watch too carefully what they say for fear of offending others. This means these types try not to be too thin-skinned, taking jokes with a grain of salt. However, they are very conscious of the fact that the way something is said is very important to how it will be received, so they tend to add emphasis, embellishments, and exaggerations here and there to keep people engaged. The best way to say something is highly dependent on the situation and the implied purpose of the exchange, so of course levity is not appropriate in some situations.
Even after explosive arguments, these types find it hard to hold grudges, and can tolerate people they in principle don't like, as long as the situation is primarily social and doesn't require too close contact. They prefer misgivings to be out in the open; they believe that the silent treatment is one of the worst things you can do to a person, and only aggravates the underlying problem.
MBTI,
Fi: Seeks harmony of action and thoughts with personal values. May not always articulate those values.
vs
Socionics,
Fi: Introverted ethics is an introverted, rational, and static information element. It is also called Fi, R, relational ethics, or white ethics. Fi is generally associated with the ability to gain an implicit sense of the subjective 'distance' between two people, and make judgments based off of said thing. Types with valued Fi strive to make and maintain close, personal relationships with their friends and family. They value sensitivity to others' feelings, and occasionally will make their innermost feelings and sentiments known in order to test the possibility of creating closeness with others.
Also, these types convey emotions in terms of how they were affected by something (such as "I did not like that"), rather than an extroverted ethics (Fe) approach that would describe the object itself without clear reference to the subject involved (such as "That sucked"). Much of their decisions are based on how they themselves, or others in relation to them personally, feel in contrast to considering how "the big picture" is affected (such as groups of people).
(More information on socionics and their functions:
Socionics - the16types.info - Information Elements: Descriptions by Functions )