schnappen
to snap at
To grab something or someone quickly and suddenly.
Der Hund schnappte nach dem Ball, den ich geworfen hatte.
The dog snapped at the ball that I had thrown.

to snap / grab
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to snap at
To grab something or someone quickly and suddenly.
Der Hund schnappte nach dem Ball, den ich geworfen hatte.
The dog snapped at the ball that I had thrown.

When 'schnappen' (to snap/grab) describes a quick movement toward something, it is often used with the preposition 'nach' and the dative. This emphasizes the attempt to grab something.
Das Krokodil schnappte nach dem Fleisch, aber verfehlte es.
The crocodile snapped at the meat but missed it.
The phrase 'sich (dative) etwas (accusative) schnappen' means to quickly take something for oneself, often before others do. It is a very common, slightly colloquial expression.
Schnapp dir eine Jacke, es wird langsam kalt draußen.
Grab a jacket; it's starting to get cold outside.
The expression 'nach Luft schnappen' (to gasp for air) is a fixed idiom. It is used when someone breathes in sharply because of exertion, shock, or shortness of breath.
Als er die Rechnung sah, musste er kurz nach Luft schnappen.
When he saw the bill, he had to gasp for air for a moment.
In connection with crime and the police, 'schnappen' (to nab) is a colloquial word for 'festnehmen' (to detain) or 'verhaften' (to arrest). It is not used in official contexts such as police reports.
Die Kommissarin war entschlossen, den Täter zu schnappen.
The detective was determined to nab the culprit.
To express that something closes suddenly and often with a sound, 'schnappen' (to snap) is combined with the particle 'zu'. 'Zuschnappen' (to snap shut) can also be seen as a separate separable verb.
Die Falle schnappte zu, aber die Maus war schon weg.
The trap snapped shut, but the mouse was already gone.
to take
'nehmen' and 'schnappen' can both mean grabbing something or taking something for yourself. 'nehmen' is the normal, neutral word. It fits almost all everyday situations. 'schnappen' emphasizes that something happens quickly, suddenly, or a bit hastily. It often sounds colloquial as well. You can say 'Ich nehme meine Jacke' (I'm taking my jacket) when it is calm and normal. 'Ich schnappe mir meine Jacke' (I'll grab my jacket) sounds faster, for example because you have to leave right away. The words are easy to confuse because they describe a similar action, but 'schnappen' has more speed and energy.

Vor dem Regen schnappt sich Lisa schnell ihre Tasche und rennt zum Bus.
Before the rain starts, Lisa quickly grabs her bag and runs to the bus.
Nimm bitte den blauen Stift, der auf dem Tisch liegt.
Please take the blue pen that's on the table.