I know it is not a question about the Portuguese language however I am curious to know these words differences:
Professor Explicador Formador Docente
centro de explicações centro de estudos Centro Pedagógico
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Professor. A teacher in the professional sense of the word, mostly used in the context of institutional education. Seldomly used to refer to someone with abundant knowledge and some position of teaching outside of institutional education.
Explicador. A tutor, in the commercial sense of the word. Refers to someone giving private lessons outside of institutional teaching, frequently to help students better their academic performance within institutional teaching. Can be applied to someone who only teaches a few lessons or to someone who tutors the same student for several years.
Formador. A commercial lecturer. Refers to someone who teaches a course or class on a professional or technical subject outside the scope of the regular schooling system. Modern EU laws require a "Formador" to have undertaken a formal certification of some kind, can be independent of formal higher education.
Docente. A lecturer within the schooling system. More frequently applied to teachers in higher education, less frequently used -although validly- as a synonym for teachers of school degrees preceding higher education.
Centro de explicações. A commercial business space having several tutors.
Centro Pedagógico. Same as the above, with a more modern wording (explicações being an older more traditional word, sometimes with an almost informal or non-commercial sense, eg: "My neighboor tutors me in biology").
Centro de estudos. Two possible senses. Can be the same as the above, or can also refer to an expert study group within a larger academic and professional organization.