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.

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
'der Präsident' and 'der Direktor' can both mean a leading person in an institution. However, they are different titles and do not fit everywhere. 'der Direktor' is often used for the head of a school, museum, or theater, or for a high-ranking position in a government office or company. 'der Präsident' sounds more official and is more likely to fit certain organizations, universities, associations, or other large institutions. Learners may confuse the words because both refer to a person at the top. What usually matters is which title is customary in the particular institution.

Am Morgen hat sie einen Termin beim Direktor der Schule.
In the morning, she has an appointment with the school principal.
Sie wurde Präsidentin des Verbandes, weil viele Mitglieder ihr vertrauten.
She became president of the association because many members trusted her.