
quetschen
to squeeze
To press something with strong pressure so that it loses its shape, is damaged, or liquid comes out.
Für den frischen Saft müssen wir noch ein paar Orangen quetschen.
For the fresh juice, we still need to squeeze a few oranges.
to squeeze / crush
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to squeeze
To press something with strong pressure so that it loses its shape, is damaged, or liquid comes out.
Für den frischen Saft müssen wir noch ein paar Orangen quetschen.
For the fresh juice, we still need to squeeze a few oranges.

to squeeze in
To force oneself with effort into a very tight space or manage to fit inside.
Wir mussten uns zu fünft auf die Rückbank des Kleinwagens quetschen.
The five of us had to squeeze into the back seat of the small car.

to pinch/crush
To injure a body part by strong pressure or by getting it trapped.
Pass auf, dass du dir nicht den Finger in der Tür quetschst!
Be careful not to pinch your finger in the door!
'Quetschen' (to squeeze/crush) is often used reflexively, but then it has two different structures. 'Sich quetschen' means to squeeze oneself into a tight space. 'Sich (dative) etwas (accusative) quetschen' means to trap and injure a body part.
Alle quetschten sich in den kleinen Aufzug.
Everyone squeezed into the small elevator.
In the basic meaning 'pressen' (to press), 'quetschen' (to squeeze) is often used in connection with preparing food. Typical objects are fruits or vegetables from which you want to get juice or purée.
Für das Dressing müssen wir noch eine Knoblauchzehe quetschen.
For the dressing, we still need to crush a clove of garlic.
When people force themselves into somewhere, 'sich quetschen' (to squeeze oneself in) almost always appears with a preposition that describes the tight place. Typical ones are 'in', 'auf', or 'zwischen' with the accusative.
Wir quetschten uns zu viert auf das kleine Sofa.
The four of us squeezed onto the small sofa.
to press / hug
Drücken generally means applying force to an object without necessarily deforming it. Quetschen implies greater pressure, causing the object to lose its shape, become damaged, or release liquid.

Lena quetscht die reife Tomate so stark, dass sie ihre Form verliert.
Lena squeezes the ripe tomato so hard that it loses its shape.
Lena drückt leicht auf die reife Tomate, um ihre Festigkeit zu prüfen.
Lena gently presses the ripe tomato to check how firm it is.