der Stein
stone
A solid, mineral piece of rock of varying size.
Er warf einen kleinen Stein ins Wasser.
He threw a small stone into the water.

stone
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stone
A solid, mineral piece of rock of varying size.
Er warf einen kleinen Stein ins Wasser.
He threw a small stone into the water.

'Stein' (stone) is a very productive base word in German. You can find it in many words such as 'Grundstein' (foundation stone), 'Meilenstein' (milestone), 'Edelstein' (gemstone), or 'Grabstein' (gravestone).
Die Grundsteinlegung für das neue Gebäude ist nächste Woche.
The laying of the foundation stone for the new building is next week.
As an individual object, 'der Stein' (stone) is countable (plural: 'die Steine'). As a material, 'Stein' (stone) is uncountable and is used without an article.
Die Kinder werfen Steine ins Wasser.
The children are throwing stones into the water.
In fruit, the hard core is called a 'Stein' (pit/stone). Fruits with such a core, like cherries, peaches, or apricots, are collectively called 'Steinobst' (stone fruit).
Vorsicht, die Kirschen haben noch Steine.
Careful, the cherries still have pits.
In many board games, a game piece is called a 'Stein' (piece/stone). This is the case, for example, in checkers, Nine Men's Morris, or the Asian game Go.
Wenn du jetzt nicht aufpasst, verlierst du einen Stein.
If you don't pay attention now, you'll lose a piece.
The expression 'der Stein des Anstoßes' (the sticking point / bone of contention) is a fixed idiom. It refers to the main cause of an argument or general annoyance.
Die neue Parkgebühr war der Stein des Anstoßes für die Anwohner.
The new parking fee was the sticking point for the residents.
The idiom 'einen Stein im Brett bei jemandem haben' means that someone is very popular with that person and enjoys their trust.
Seit er dem Chef geholfen hat, hat er einen Stein im Brett bei ihm.
Ever since he helped the boss, he has been in his good books.
In a medical context, 'Stein' (stone) refers to a solid deposit in the body. It is usually used as part of a compound word such as 'Nierenstein' (kidney stone) or 'Gallenstein' (gallstone).
Er hatte starke Schmerzen wegen eines Nierensteins.
He had severe pain because of a kidney stone.
core / pit / nucleus
'der Stein' and 'der Kern' can both mean the hard inner part of a fruit. 'Stein' is used especially for fruits such as cherries, peaches, or plums. In those fruits, there is usually a single hard part in the middle. 'Kern' is more general and means the inner part of a fruit, often where the seeds are. The words can be confused because both occur in the context of fruit. With stone fruits, 'Stein' sounds more natural: 'Kirschstein' (cherry pit), 'Pfirsichstein' (peach pit). 'Kern' fits better when you are talking generally about the inside or the seeds of a fruit.

Beim Essen der Kirsche habe ich fast auf den Stein gebissen.
While eating the cherry, I almost bit down on the pit.
Im Kern der Frucht liegen die Samen.
The seeds are inside the core of the fruit.