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Agarrar vs. coger

In Spanish, both agarrar and coger mean to grab or to seize (with the hand), but they are used differently depending on the region and context.

Agarrar

A1
In most Spanish-speaking countries, agarrar means to grab or to seize something with the hand. It implies a firm grip and is commonly used in everyday speech.
Agarré el vaso antes de que cayera al suelo.
(I grabbed the glass before it fell to the ground.)
No agarres eso, está caliente.
(Don't grab that, it's hot.)
El niño agarró la mano de su madre para cruzar la calle.
(The child grabbed his mother's hand to cross the street.)

Coger

B1
In Spain, coger is commonly used to mean to grab or to seize. However, in many Latin American countries, especially Mexico, Venezuela, and Uruguay, coger has a vulgar connotation and can mean to have sexual intercourse. Therefore, it is avoided in those regions in polite conversation.
Cogió el teléfono y llamó a su amigo.
(He grabbed the phone and called his friend.)
Voy a coger el autobús.
(I am going to catch the bus.)

Summary

Agarrar and coger both mean to grab or to seize, but their usage varies by region. Agarrar is widely accepted across Spanish-speaking countries with a non-vulgar implication. On the other hand, while coger is common and neutral in Spain, it has vulgar connotations in several Latin American countries and should be avoided there.