
der Korken
cork
A stopper made of cork or plastic used to close a bottle, especially a wine bottle.
Der Korken steckte so fest in der Flasche, dass ich ihn kaum herausbekam.
The cork was stuck so firmly in the bottle that I could hardly get it out.
cork / float
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cork
A stopper made of cork or plastic used to close a bottle, especially a wine bottle.
Der Korken steckte so fest in der Flasche, dass ich ihn kaum herausbekam.
The cork was stuck so firmly in the bottle that I could hardly get it out.

to pop the corks
A fixed expression meaning to celebrate exuberantly and enthusiastically, typically by opening bottles of sparkling wine or champagne.
Nach dem gewonnenen Finale haben wir die ganze Nacht die Korken knallen lassen.
After winning the final, we popped the corks all night.

float
A float made of cork that is attached to a fishing line as a bite indicator when fishing.
Er starrte konzentriert auf den Korken, der ruhig auf dem Wasser tanzte.
He stared intently at the float, which was bobbing calmly on the water.
'Der Korken' (cork/stopper) is the closure for a bottle. It is made from the material 'der Kork' (cork). So you distinguish between the object ('der Korken') and the raw material ('der Kork').
Dieser Korken ist nicht aus Kork, sondern aus Kunststoff.
This cork is not made of cork, but of plastic.
The expression 'die Korken knallen lassen' (to pop the corks) means to celebrate exuberantly. It refers to the loud sound made when opening a bottle of sparkling wine or champagne.
Zum neuen Jahr lassen wir um Mitternacht die Korken knallen.
For the New Year, we'll pop the corks at midnight.
When 'Korken' (float) is mentioned in connection with fishing, a lake, or a river, it refers to the float on the fishing line. Words like 'Wasser' (water), 'schwimmen' (to float/swim), or 'Biss' (bite) are clear signals.
Plötzlich tauchte der Korken unter Wasser – er hatte einen Fisch am Haken.
Suddenly the float dipped under the water—he had a fish on the hook.
cork
Both words can be associated with a bottle’s closure. Korken normally refers to the specific stopper, while Kork usually means the material, but it can also refer to this type of stopper. For a single stopper, Korken is generally used; for the material, Kork is used.

Der Korken der Weinflasche saß so fest, dass wir einen Öffner brauchten.
The cork in the wine bottle was stuck so tightly that we needed an opener.
Die Flasche ist mit Kork verschlossen, damit der Wein gut lagern kann.
The bottle is sealed with cork so that the wine can be stored properly.