der Durst
thirst
The physical feeling and need to drink something.
Nach dem Sport hatte ich einen riesigen Durst und trank eine ganze Flasche Wasser.
After exercising, I was extremely thirsty and drank a whole bottle of water.

thirst
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thirst
The physical feeling and need to drink something.
Nach dem Sport hatte ich einen riesigen Durst und trank eine ganze Flasche Wasser.
After exercising, I was extremely thirsty and drank a whole bottle of water.

For the physical feeling, there are fixed verb combinations. You say 'Durst haben' (to be thirsty), 'Durst bekommen' (to become/get thirsty), or 'seinen Durst löschen' (to quench one's thirst).
Nach der langen Wanderung hatten wir großen Durst.
After the long hike, we were very thirsty.
In the figurative meaning, 'Durst' (thirst) is always used with the preposition 'nach' and the dative. It describes a strong desire for something abstract.
Sein Durst nach Abenteuern war unstillbar.
His thirst for adventure was unquenchable.
In its main meaning, 'Durst' (thirst) is used as an uncountable noun and normally has no plural form. You do not speak of 'vielen Dürsten' (many thirsts).
Bei dieser Hitze ist Durst ein ständiger Begleiter.
In this heat, thirst is a constant companion.
hunger
'der Hunger' and 'der Durst' both describe a physical need. 'Hunger' means that you need to eat something. 'Durst' means that you need to drink something. They can be confused because both often occur together and are used in similar ways, for example with 'haben'. In a figurative meaning, both can express a strong desire: 'Hunger nach Erfolg' (hunger for success) or 'Durst nach Wissen' (thirst for knowledge). Still, the difference remains important: Hunger belongs to eating, thirst to drinking.

Nach dem Lauf ist Marias Durst stärker als ihr Hunger.
After the run, Maria's thirst is stronger than her hunger.
Im Zug wurde Daniels Hunger so groß, dass er ein Brötchen kaufte.
On the train, Daniel's hunger grew so strong that he bought a bread roll.