
der Sattel
saddle
A seat for a rider on the back of a horse or another riding animal.
Sie legte dem Pferd den Sattel auf und zog den Gurt fest.
She put the saddle on the horse and tightened the girth.
saddle
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saddle
A seat for a rider on the back of a horse or another riding animal.
Sie legte dem Pferd den Sattel auf und zog den Gurt fest.
She put the saddle on the horse and tightened the girth.

seat / saddle
The seat on a bicycle or motorcycle.
Nach einer langen Radtour tat mir der harte Sattel weh.
After a long bike ride, the hard saddle made me sore.

to be firmly in the saddle
To hold a secure, unchallenged position in an office or role.
Trotz der internen Kritik sitzt die Chefin weiterhin fest im Sattel.
Despite the internal criticism, the boss is still firmly in the saddle.

saddle
In geography, a dip or pass between two mountain peaks.
Vom Sattel aus hatten wir eine wunderbare Aussicht in beide Täler.
From the saddle, we had a wonderful view into both valleys.
The verb 'satteln' (to saddle) is derived from the noun 'der Sattel' (saddle). It means to put a saddle on a horse. The expression 'umsatteln' (to change saddles) means, figuratively, to change one’s profession or field.
Bevor wir losreiten können, müssen wir die Pferde satteln.
Before we can ride off, we have to saddle the horses.
The idiom 'fest im Sattel sitzen' (to be firmly in the saddle) means to have a very secure and unchallenged professional or political position. The image is that of a rider who cannot fall off the horse.
Obwohl es viel Kritik gab, sitzt der Minister weiterhin fest im Sattel.
Although there was a lot of criticism, the minister is still firmly in the saddle.
You can tell which meaning of 'Sattel' (saddle) is intended from the context. Words like 'Pferd' (horse) or 'reiten' (to ride) point to a riding saddle, 'Fahrrad' (bicycle) to a bicycle seat, and 'Berg' (mountain) or 'Gipfel' (peak) to the geographical form.
Der Sattel meines Fahrrads ist sehr unbequem.
The saddle on my bike is very uncomfortable.
In connection with horses, typical expressions are 'den Sattel auflegen' (to put on the saddle) or simply 'im Sattel sitzen' (to sit in the saddle). The person riding is also referred to as a 'Reiter im Sattel' (rider in the saddle).
Schon als Kind saß sie sicher im Sattel.
Even as a child, she sat securely in the saddle.
seat / headquarters
Sitz is the general term for a place to sit. Sattel, by contrast, refers specifically to the seat on a riding animal, bicycle, or motorcycle. Use Sitz for a place in a car or bus, and Sattel when riding or cycling.

Vor der Fahrt stellt sie den Sattel am Fahrrad richtig ein.
Before the ride, she adjusts the saddle on the bicycle properly.
Vor der Fahrt stellt sie den Sitz im Auto richtig ein.
Before the journey, she adjusts the seat in the car properly.