bändigen
to tame
To tame a wild animal or bring it under control.
Der Dompteur versuchte, den Löwen zu bändigen.
The animal trainer tried to tame the lion.

to tame / control
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to tame
To tame a wild animal or bring it under control.
Der Dompteur versuchte, den Löwen zu bändigen.
The animal trainer tried to tame the lion.

The verb 'bändigen' (to tame/control) is related to 'das Band' (ribbon/band) and 'binden' (to bind/tie). The literal idea is to symbolically put a band around something wild or chaotic in order to control it.
Es war unmöglich, die tobende Menschenmenge zu bändigen.
It was impossible to control the raging crowd.
'Bändigen' (to tame/control) is always used with an accusative object. You ask: whom or what are you taming/controlling? This also applies to the reflexive form 'sich bändigen' (to control oneself), where the reflexive pronoun is the accusative object.
Der Reiter konnte das scheue Pferd nur mit Mühe bändigen.
The rider could only tame the skittish horse with difficulty.
'Bändigen' (to tame/control) is a rather strong and vivid word. It is often used in contexts involving great force or intense chaos, and can therefore sound somewhat elevated or dramatic.
Die Regierung versucht, die Inflation zu bändigen.
The government is trying to control inflation.
In its figurative meaning, 'bändigen' (to control) is often used for forces of nature ('das Feuer' — fire, 'eine Flut' — a flood), strong emotions ('die Wut' — anger, 'die Leidenschaft' — passion), or even something everyday like unruly hair.
Mit diesem Gel kann ich endlich meine Haare bändigen.
With this gel, I can finally control my hair.
to check / control
'kontrollieren' and 'bändigen' can both mean bringing something under control. 'kontrollieren' is more neutral and can be used more broadly. It can refer to a situation, a person, a device, or your own feelings. 'bändigen' sounds stronger: something is wild, chaotic, or very difficult to control. For example, you 'bändigt' a wild animal, strong feelings, a crowd, or a fire. The words can be confused because both express control. If it is only about normal steering or controlling, 'kontrollieren' fits. If something is very intense or hard to stop, 'bändigen' is more precise.

Die Feuerwehr versucht, das Feuer im Wald zu bändigen.
The fire department is trying to bring the forest fire under control.
Der Verkäufer kontrolliert die Kasse am Ende des Tages.
The salesperson checks the cash register at the end of the day.