If two partners are separated, they are not living together any more as a couple. They may still be married; separated is not the same as divorced. People use it on official forms (single, married, separated, divorced) and in careful talk about family life. It can be a planned legal step, or a quieter fact: they have different homes now. Say it kindly — it is a living situation, not a score. Though actually, English also uses separated in a plainer way (“the teacher separated the two groups”), but this entry is the relationship meaning.