die Eiche
oak
A large, long-lived deciduous tree with characteristically shaped leaves and acorns as its fruit.
Unter der alten Eiche im Park machen wir oft ein Picknick.
We often have a picnic under the old oak in the park.

oak
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oak
A large, long-lived deciduous tree with characteristically shaped leaves and acorns as its fruit.
Unter der alten Eiche im Park machen wir oft ein Picknick.
We often have a picnic under the old oak in the park.

The oak has strong symbolic meaning in German culture. It stands for strength, longevity, and stability and is sometimes referred to as the 'deutsche Eiche' (German oak).
Das Eichenblatt war früher auf deutschen Münzen abgebildet.
The oak leaf used to be depicted on German coins.
The context tells you whether the tree or the wood is meant. If people are talking about nature, gardens, or forests, they mean the tree. If it is about furniture, floors, or materials, they mean the wood.
Im Herbst fallen die Blätter von der Eiche.
In autumn, the leaves fall from the oak.
'Eiche' (oak) is often the first part of compound nouns. These usually refer to parts of the tree or products made from its wood, such as 'das Eichenblatt' (the oak leaf), 'der Eichenwald' (the oak forest), or 'das Eichenfass' (the oak barrel).
Der Wein reifte mehrere Jahre in einem Eichenfass.
The wine matured for several years in an oak barrel.
When referring to the wood, typical combinations are 'aus massiver Eiche' (made of solid oak) or 'aus Eiche gefertigt' (crafted from oak). A well-known, somewhat old-fashioned furnishing style is called 'Eiche rustikal' (rustic oak).
Die Kommode ist aus massiver Eiche und daher sehr schwer.
The chest of drawers is made of solid oak and is therefore very heavy.
beech
'die Buche' and 'die Eiche' are both large deciduous trees, and both words can also refer to the wood of these trees. That is why they can easily be confused, especially when talking about furniture, floors, or forests. But they are different tree species. An oak can often be recognized by its acorns, while a beech tree has smooth gray bark. For the wood as well, 'Buche' means beechwood and 'Eiche' means oak. If the exact type of tree or wood is important, you should use the appropriate word.

Zur Vorbereitung auf den Ausflug liest sie in der Bibliothek etwas über die Eiche und ihre Früchte.
To prepare for the trip, she reads something about the oak and its fruit in the library.
Neben dem Weg steht eine alte Buche mit glatter grauer Rinde.
Next to the path stands an old beech tree with smooth gray bark.