
der Direktor
principal
The person who runs a school.
Der Direktor hat heute Morgen eine Durchsage für alle Klassen gemacht.
The principal made an announcement for all classes this morning.
director / principal
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principal
The person who runs a school.
Der Direktor hat heute Morgen eine Durchsage für alle Klassen gemacht.
The principal made an announcement for all classes this morning.

director
A leading person in a company, government office, museum, theater, or other institution.
Der Direktor des Museums führte uns persönlich durch die neue Ausstellung.
The director of the museum personally guided us through the new exhibition.
The word belongs to the word family around 'dirigieren' (to direct, to lead). Also related is 'die Direktion' (management/administration), which can refer both to the management level and to the director's or principal's office.
Bitte melde dich morgen in der Direktion.
Please report to the principal's office tomorrow.
To specify what a person leads, German usually uses the genitive or the preposition 'von' (of/from). For example: 'der Direktor der Schule' (the principal of the school) or 'der Direktor des Museums' (the director of the museum).
Der Direktor der Bank hielt eine Rede.
The director of the bank gave a speech.
In a school context, the phrasing 'zum Direktor müssen' (to have to go to the principal) or 'vom Direktor gerufen werden' (to be called by the principal) is very common. It usually means that a student has caused trouble.
Wenn du dich weiter so benimmst, musst du zum Direktor!
If you keep behaving like that, you'll have to go to the principal!
president
Präsident and Direktor can both refer to the person who leads an institution or organization. Präsident is the relevant official title, while Direktor is used especially for the head of a school or other institutions. The deciding factors are therefore the institution’s structure and the official title.

Der Direktor der Stiftung stellte bei der Versammlung den Jahresbericht vor.
The director of the foundation presented the annual report at the meeting.
Der Präsident der Stiftung stellte bei der Versammlung den Jahresbericht vor.
The president of the foundation presented the annual report at the meeting.