
der Föhn
hair dryer
An electrical device that produces a stream of warm air to dry hair.
Ich muss mir noch schnell mit dem Föhn die Haare trocknen, bevor wir gehen.
I quickly need to dry my hair with the hair dryer before we go.
hair dryer / foehn
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hair dryer
An electrical device that produces a stream of warm air to dry hair.
Ich muss mir noch schnell mit dem Föhn die Haare trocknen, bevor wir gehen.
I quickly need to dry my hair with the hair dryer before we go.

foehn wind
A warm, dry downslope wind that occurs especially often on the northern side of the Alps.
Wenn der Föhn weht, klagen viele Menschen in den Alpentälern über Kopfschmerzen.
When the foehn wind blows, many people in the Alpine valleys complain of headaches.
The context tells you whether the device or the wind is meant. If you are talking about hair, the bathroom, or electrical appliances, it means the hair dryer. If it is about weather, the Alps, wind, or headaches, it means the weather phenomenon.
Kannst du mir den Föhn geben? Meine Haare sind noch nass.
Can you give me the hair dryer? My hair is still wet.
The verb 'föhnen' (to blow-dry) is derived from the noun 'der Föhn' (hair dryer). So you can say: 'Ich trockne meine Haare mit dem Föhn' (I dry my hair with the hair dryer) or, more briefly: 'Ich föhne meine Haare' (I blow-dry my hair).
Nach dem Schwimmen föhne ich mir immer die Haare.
After swimming, I always blow-dry my hair.
The foehn wind as a weather phenomenon is often associated with physical discomfort. Typical statements are that you 'bei Föhn Kopfschmerzen hat' (have headaches when there is a foehn wind) or 'sich wegen des Föhns unwohl fühlt' (feel unwell because of the foehn wind).
Meine Großmutter spürt den Föhn immer in ihren Gelenken.
My grandmother always feels the foehn wind in her joints.
dryer
Trockner can generally refer to a device used for drying, but without any further specification it usually means a clothes dryer. Föhn is the usual standalone term for a device used to dry hair. Trockner is therefore used for laundry, while Föhn is used for hair.

Nach dem Waschen trocknet Mia ihre nassen Haare mit dem Föhn.
After washing her hair, Mia dries it with the hair dryer.
Nach dem Waschen kommen die nassen Handtücher in den Trockner.
After washing them, the wet towels go in the dryer.