"The women and men are teachers."
Translation:A nők és férfiak tanárok.
Not sure what you mean about the definite article, I see only one here. But anyway, it makes no difference whether you use "tanító" or "tanár".
"Tanító" is usually used for teachers in elementary schools, probably in the first four years. Later, as school becomes more "serious", "teacher" is the usual word.
They are thus slightly different professions. A "tanító" usually teaches everything to his or her students, at a basic level. They then move on to higher classes and meet the more specialized "tanárok".
There are distinct schools for training the two professions.
Other than that, "tanító" can be used for a person who is not necessarily a teacher by profession but someone who educates or influences a lot of people through his or her speeches, writing or whole life.