der Schwanz
tail
The movable rear body appendage found in many vertebrates.
Die Katze putzt sich ausgiebig den Schwanz.
The cat is thoroughly cleaning its tail.

tail / dick
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tail
The movable rear body appendage found in many vertebrates.
Die Katze putzt sich ausgiebig den Schwanz.
The cat is thoroughly cleaning its tail.

The meaning of 'Schwanz' (tail/dick) is almost always clear from the context. When talking about animals, it means the body appendage. For objects such as comets or airplanes, it means the rear part.
Der Hund wedelte freudig mit dem Schwanz.
The dog wagged its tail happily.
There are fixed expressions connected with animals. 'Mit dem Schwanz wedeln' (to wag one's tail) means joy, especially in dogs. 'Den Schwanz einziehen' (to tuck one's tail in) means that someone is afraid or submits.
Als der große Hund bellte, hat der kleine sofort den Schwanz eingezogen.
When the big dog barked, the little one immediately tucked its tail in.
The meaning 'Penis' (penis) is vulgar and belongs to colloquial or obscene language. Using it in normal conversations or in formal contexts is inappropriate and can be perceived as offensive.
Der Betrunkene rief vulgäre Wörter wie „Schwanz“ über die Straße.
The drunk shouted vulgar words like 'Schwanz' (dick) across the street.
The idiom 'einen Rattenschwanz nach sich ziehen' means that an action has a long chain of negative and often unforeseen consequences. The structure is usually fixed.
Die Schließung der Fabrik zog einen Rattenschwanz an wirtschaftlichen Problemen nach sich.
The closure of the factory brought a whole chain of economic problems with it.
penis
'der Schwanz' and 'der Penis' can both refer to a male sex organ. 'Penis' is the neutral, factual word for this, for example at the doctor’s office or in biology class. However, 'Schwanz' first has the normal meaning of the rear body part of animals. When 'Schwanz' means the sex organ, it is vulgar and does not fit polite or factual situations. Learners should therefore be careful: for animals, 'Schwanz' is normal; for the human body, 'Penis' is usually the safe choice.

Der Hund wedelt mit dem Schwanz, wenn er sich freut.
The dog wags its tail when it is happy.
Im Biologieunterricht erklärt die Lehrerin, welche Funktion der Penis hat.
In biology class, the teacher explains what function the penis has.