die Buche
beech tree
A large deciduous tree with smooth, gray bark that is widespread in European forests.
Unter der alten Buche im Garten haben wir eine Bank aufgestellt.
We set up a bench under the old beech tree in the garden.

beech
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beech tree
A large deciduous tree with smooth, gray bark that is widespread in European forests.
Unter der alten Buche im Garten haben wir eine Bank aufgestellt.
We set up a bench under the old beech tree in the garden.

The word 'Buche' (beech) is historically related to the word 'Buch' (book). In the past, writing was carved into tablets made of beechwood, which is how the name for the book developed.
Die germanischen Runen wurden oft in Buchenholz geschnitzt.
Germanic runes were often carved into beechwood.
The context tells you whether the tree or the material is meant. If it is about forests, gardens, or leaves, it is the tree. If it is about furniture, floors, or objects, the wood is meant.
Im Herbst färben sich die Blätter der Buche bunt.
In autumn, the leaves of the beech tree turn colorful.
When 'Buche' (beechwood) describes the wood as a material, it is often used without an article, especially after the preposition 'aus' (made of/from). This is typical for many material terms in German.
Der Boden in unserer Wohnung ist aus Buche.
The floor in our apartment is made of beechwood.
oak
'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.

Neben dem Weg steht eine alte Buche mit glatter grauer Rinde.
Next to the path stands an old beech tree with smooth gray bark.
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.