
die Mähne
mane
The long, thick hair on the neck and back of the neck of certain animals, especially horses or lions.
Das Pferd schüttelte seine prächtige Mähne.
The horse shook its magnificent mane.
mane
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mane
The long, thick hair on the neck and back of the neck of certain animals, especially horses or lions.
Das Pferd schüttelte seine prächtige Mähne.
The horse shook its magnificent mane.

mane
Colloquially and often slightly jokingly used for long, thick, and sometimes messy hair on a person's head.
Nach dem Aufstehen musste er erst einmal seine wilde Mähne bändigen.
After getting up, he first had to tame his wild mane.
You can always tell from the context whether the hair of an animal or a person is meant. If people are talking about a horse or a lion, the meaning is literal. If they are talking about a person, it is a colloquial exaggeration.
Der Löwe im Zoo hatte eine beeindruckende Mähne.
The lion at the zoo had an impressive mane.
Using 'Mähne' (mane) for human hair is colloquial and often meant slightly jokingly or admiringly. In formal texts, you would not use it for people.
Deine Tochter hat ja eine richtige Löwenmähne!
Your daughter really has a lion's mane!
In connection with animals, 'Mähne' (mane) is often used with verbs like 'schütteln' (to shake) or 'kämmen' (to comb), and adjectives like 'dicht' (thick), 'lang' (long), or 'prächtig' (magnificent).
Die Reiterin bürstete die dichte Mähne ihres Pferdes.
The rider brushed her horse's thick mane.
When 'Mähne' (mane) is used for human hair, typical expressions are 'seine Mähne bändigen' (to tame one's mane) or 'eine wilde Mähne haben' (to have a wild mane).
Mit diesem Kamm versuche ich jeden Morgen, meine wilde Mähne zu bändigen.
With this comb, I try every morning to tame my wild mane.
hair
Haar refers neutrally to the hair on a person’s head. Mähne is colloquial and slightly humorous, and can refer to hair that is especially long, thick, or somewhat messy. Without this striking or humorous effect, Haar is the better choice.

Nach dem windigen Spaziergang hängt ihm seine lange Mähne wild ins Gesicht.
After his windy walk, his long mane hangs wildly over his face.
Nach dem Friseurbesuch fällt ihr langes Haar glatt über die Schultern.
After her visit to the hairdresser, her long hair falls smoothly over her shoulders.