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.
'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.
closure / fastener
'der Verschluss' and 'der Korken' can both refer to something used to close an opening. 'Verschluss' is the general term and fits many things, for example bottles, bags, or clothing. 'Korken' is a specific stopper for bottles, especially wine bottles, and is often made of cork or plastic. The words can be confused because a cork is a kind of closure. But not every closure is a cork. For a wine bottle, 'Korken' is more precise; for other kinds, people usually say 'Verschluss'.
Nach dem Essen zog Paul den Korken aus der Weinflasche.
After the meal, Paul pulled the cork out of the wine bottle.
Der Verschluss der Sporttasche lässt sich nur schwer öffnen.
The closure on the sports bag is hard to open.