die Diät
diet
A special way of eating that aims to reduce body weight or that is followed for medical reasons.
Nach den Feiertagen fangen viele Menschen eine Diät an.
After the holidays, many people start a diet.

diet / allowance
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diet
A special way of eating that aims to reduce body weight or that is followed for medical reasons.
Nach den Feiertagen fangen viele Menschen eine Diät an.
After the holidays, many people start a diet.

In German, 'Diät' is strongly associated with the intention of losing weight. The neutral English meaning 'diet' (general way of eating) is usually expressed in German with 'die Ernährung' (nutrition/diet).
Ich mache gerade eine Diät, um ein paar Kilo abzunehmen.
I'm currently on a diet to lose a few kilos.
The meanings are clearly separate. In the singular, 'Diät' almost always refers to nutrition or dieting. The plural form 'Diäten' refers almost exclusively to politicians' salaries or allowances.
Wegen seiner Allergie muss er eine strenge Diät einhalten.
Because of his allergy, he has to follow a strict diet.
The most common verbs related to a weight-loss diet are 'eine Diät machen' (to go on a diet), 'auf Diät sein' (to be on a diet), or 'eine Diät beginnen' (to start a diet).
Seit Januar ist er auf Diät und hat schon fünf Kilo verloren.
He has been on a diet since January and has already lost five kilos.
In the meaning 'Abgeordnetenbezüge' (parliamentary compensation), this word is used almost exclusively in the plural, 'die Diäten' (parliamentary allowances). The singular form 'die Diät' is unusual in this context.
Die Höhe der Diäten ist gesetzlich festgelegt.
The amount of the parliamentary allowances is set by law.
nutrition / diet
'Ernährung' and 'Diät' can both describe how someone eats. 'Ernährung' is the general word and fits normal eating habits, health, and lifestyle. In German, 'Diät' usually means a special way of eating, often for losing weight or for medical reasons. For the general meaning of 'diet', German usually says 'Ernährung', not 'Diät'. That is why the risk of confusion is high: not every 'Ernährung' is a 'Diät', but a 'Diät' is a special form of 'Ernährung'.

Sie macht eine Diät, weil ihr Arzt ihr das empfohlen hat.
She is on a diet because her doctor recommended it.
Eine ausgewogene Ernährung ist für Kinder besonders wichtig.
A balanced diet is especially important for children.