der Wedel
frond
A large, often fan-shaped leaf, especially of ferns or palms.
Die Palmwedel raschelten im Wind.
The palm fronds rustled in the wind.

frond / duster / tail
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frond
A large, often fan-shaped leaf, especially of ferns or palms.
Die Palmwedel raschelten im Wind.
The palm fronds rustled in the wind.

All meanings of 'der Wedel' (frond / duster / tail) are connected to the verb 'wedeln' (to wag or wave something back and forth). A palm frond moves in the wind, you wipe with a duster, and an animal wags its tail.
Der Hund wedelte freudig mit dem Schwanz.
The dog wagged its tail happily.
The context makes clear which 'Wedel' (frond / duster / tail) is meant. If it is about plants, it means the leaf. If it is about cleaning, it means a duster. And with animals like foxes, it means the tail.
Die Blätter der Palme sind riesige Wedel.
The leaves of the palm tree are huge fronds.
In the meaning of 'Staubwischgerät' (dusting tool), the compounds 'der Staubwedel' (duster) or 'der Federwedel' (feather duster) are often used. Typical verbs are 'Staub wischen' (to dust) or 'entstauben' (to remove dust).
Sie entfernte den Staub auf den Büchern mit einem Federwedel.
She removed the dust from the books with a feather duster.
The term 'Wedel' for an animal's tail is technical language used by hunters (hunting terminology). In normal usage, people simply say 'der Schwanz' (the tail).
Der Fuchs war im Gebüsch kaum zu sehen, nur sein Wedel schaute heraus.
The fox was barely visible in the bushes; only its tail was sticking out.
tail / dick
'Schwanz' and 'Wedel' can both mean the rear body part of an animal. 'Schwanz' is the normal general word and fits most animals. 'Wedel' is much more specific and is used mainly in hunting terminology for the bushy tail of certain animals, for example a fox or squirrel. The words can be confused because they can refer to the same body part. In everyday language, you almost always say 'Schwanz'. 'Wedel' sounds more technical or very specific and does not fit every animal.

Der Fuchs verschwand schnell im Wald, nur sein roter Wedel war noch zu sehen.
The fox quickly disappeared into the forest; only its red bushy tail could still be seen.
Im Park wedelt der Hund freundlich mit dem Schwanz.
In the park, the dog wags its tail in a friendly way.