der Nussbaum
walnut tree
A tree that bears nuts; in the narrower and most common sense, a walnut tree.
Im Herbst ernten wir die Walnüsse von dem großen Nussbaum im Garten.
In autumn, we harvest the walnuts from the large walnut tree in the garden.

walnut tree / walnut wood
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walnut tree
A tree that bears nuts; in the narrower and most common sense, a walnut tree.
Im Herbst ernten wir die Walnüsse von dem großen Nussbaum im Garten.
In autumn, we harvest the walnuts from the large walnut tree in the garden.

The word is a simple compound of 'die Nuss' (nut) and 'der Baum' (tree). So it literally refers to a tree on which nuts grow.
Unter dem alten Nussbaum haben wir eine Bank aufgestellt.
We set up a bench under the old walnut tree.
You can easily tell from the context whether the tree or the wood is meant. If you are talking about gardens, nature, or harvesting, the tree is meant. If you are talking about furniture, floors, or craftsmanship, the wood is meant.
Im Frühling blüht der Nussbaum wunderschön.
In spring, the walnut tree blooms beautifully.
When 'Nussbaum' (walnut wood) refers to the wood, it is a material name. In this case, it is often used without an article, especially after the preposition 'aus' (made of/from).
Die Kommode ist aus massivem Nussbaum.
The chest of drawers is made of solid walnut wood.