geschieden
divorced
Describing the marital status of a person whose marriage has been legally dissolved.
Meine Tante ist seit fünf Jahren geschieden und lebt jetzt allein.
My aunt has been divorced for five years and now lives alone.

divorced / separate
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divorced
Describing the marital status of a person whose marriage has been legally dissolved.
Meine Tante ist seit fünf Jahren geschieden und lebt jetzt allein.
My aunt has been divorced for five years and now lives alone.

'Geschieden' (divorced/separated) is the past participle of the verb 'scheiden' (to separate), which means 'to separate.' It is used like a normal adjective to describe a state that has resulted from a separation.
Nach einer langen Trennungsphase sind sie nun offiziell geschieden.
After a long period of separation, they are now officially divorced.
When 'geschieden' (divorced/separated) refers to people, it almost always means that their marriage has ended. When it refers to abstract things or ideas, it means 'separate' and is used in a very formal or philosophical context.
Meine Eltern sind geschieden, verstehen sich aber gut.
My parents are divorced, but they get along well.
To express marital status, you use the form '[person] ist geschieden' ([person] is divorced). If you want to say from whom, use the preposition 'von' (from): 'Sie ist von ihrem Mann geschieden' (She is divorced from her husband).
Er ist seit letztem Jahr von seiner Frau geschieden.
He has been divorced from his wife since last year.
Several related words belong to the topic of the end of a marriage: the verb is 'sich scheiden lassen' (to get divorced), the noun is 'die Scheidung' (the divorce), and the state is 'geschieden sein' (to be divorced).
Sie haben sich nach zehn Jahren Ehe scheiden lassen.
They got divorced after ten years of marriage.
different / various
'verschieden' and 'geschieden' look similar and sound similar, but they usually mean something completely different. 'verschieden' is used when things are not the same or when you are talking about several different things. 'geschieden' mainly describes a person whose marriage has legally ended. In very formal language, 'geschieden' can also mean 'separated' or 'distinguished', but in everyday life people usually think of marital status. So the typical confusion comes from the form of the words, not from their normal meaning.

Mein Nachbar ist seit zwei Jahren geschieden.
My neighbor has been divorced for two years.
Im Kurs haben die Teilnehmer verschiedene Gründe, Deutsch zu lernen.
In the course, the participants have various reasons for learning German.