hetzen
to rush
To hurry a lot or urge someone to hurry, often in a stressful and frantic way.
Ich muss jetzt hetzen, um den Zug noch zu erwischen.
I have to rush now to still catch the train.

to rush / to incite
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to rush
To hurry a lot or urge someone to hurry, often in a stressful and frantic way.
Ich muss jetzt hetzen, um den Zug noch zu erwischen.
I have to rush now to still catch the train.

You can recognize the meaning of 'hetzen' from the context. If it is about time pressure, it means 'sich beeilen' (to hurry). If the word appears with 'gegen' (against) and a group of people, it means 'Hass verbreiten' (to spread hatred). In connection with animals and hunting, the original meaning is intended.
Er hetzte zum Termin, weil er schon spät dran war.
He rushed to the appointment because he was already running late.
When 'hetzen' means 'sich beeilen' (to hurry), it always also expresses great stress and urgency. It is stronger than 'sich beeilen' and can also be used transitively to express that you are pushing someone to hurry.
Hetz mich nicht so, ich brauche noch fünf Minuten!
Don't rush me like that; I still need five minutes!
In the meaning 'Hass verbreiten' (to spread hatred), 'hetzen' is always used with the preposition 'gegen' (against) and the accusative. This structure is a clear signal for this negative meaning.
Der Redner hetzte in seiner Rede gegen die Regierung.
The speaker incited against the government in his speech.
The meaning 'jagen' (to hunt) is rare today and is used almost only in the specific context of hunting or in historical descriptions.
In alten Geschichten wird oft beschrieben, wie Wölfe die Rehe hetzen.
Old stories often describe how wolves hunt deer.
to run
'rennen' and 'hetzen' can both mean that someone is moving very quickly or is in a great hurry. 'rennen' usually describes the physical movement: someone is running fast. Colloquially, it can also mean that someone has to rush somewhere. 'hetzen' puts more emphasis on stress, pressure, and restlessness. You can 'hetzen' yourself, but you can also 'jemanden hetzen', meaning to push someone to hurry. Learners may confuse the words because both have to do with haste. 'rennen' fits better for fast movement, while 'hetzen' fits better for a stressful feeling or pressure.

Morgen müssen wir bei der Arbeit nicht so hetzen, weil der Termin verschoben wurde.
Tomorrow we won't have to rush so much at work because the appointment has been postponed.
Am Bahnhof rennt der Arzt zum Zug, weil er spät dran ist.
At the train station, the doctor runs to the train because he is running late.