die Box
box
A container, usually box-shaped, for storing or transporting objects.
Ich habe die alten Fotos in einer Box auf dem Dachboden verstaut.
I stored the old photos in a box in the attic.

box
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box
A container, usually box-shaped, for storing or transporting objects.
Ich habe die alten Fotos in einer Box auf dem Dachboden verstaut.
I stored the old photos in a box in the attic.

'Box' is a loanword from English. It has been fully integrated into the German language and, like many one-syllable loanwords, has taken the feminine article 'die'.
Kannst du mir bitte die Box mit den Werkzeugen geben?
Can you please give me the box with the tools?
Which meaning of 'Box' is intended is almost always clear from context. If you're talking about music, it means a speaker; if you're talking about the internet, it means the router.
Die Musik klingt super, du hast echt gute Boxen!
The music sounds great; you really have good speakers!
As a container, 'Box' is often part of a compound that describes the purpose more precisely. Examples are 'Aufbewahrungsbox' (storage box), 'Transportbox' (transport box), or 'Brotdose' (lunch box, literally a special box for bread).
Für den Umzug brauchen wir noch einige stabile Transportboxen.
We still need a few sturdy transport boxes for the move.
When 'Box' means a speaker, it is rather colloquial. In technical descriptions or specialist stores, the word 'Lautsprecher' (speaker) is usually used.
Schließ mal dein Handy an die Boxen an!
Connect your phone to the speakers!
In this context, 'Box' refers to a clearly separated area. For horses it is the 'Pferdebox' (horse stall), and in motorsports the 'Boxengasse' (pit lane) is the area for the 'Boxenstopp' (pit stop).
Das Rennauto muss zum Reifenwechsel an die Box.
The race car has to go to the pit for a tire change.
box / crate
'die Box' and 'der Kasten' can both mean a rectangular container in which you store or transport things. 'Box' often sounds more modern and is commonly used for smaller, practical containers made of plastic, cardboard, or fabric. 'Kasten' sounds a bit more general and often more solid or larger, for example made of wood, metal, or plastic. Learners may confuse the words because both can look like a container with straight sides. If it is about practical storage, 'Box' often fits. If the container seems more sturdy, heavy, or traditional, 'Kasten' sounds more natural.

Für die alten Fotos habe ich eine kleine Box gekauft.
I bought a small box for the old photos.
Im Keller steht ein schwerer Kasten mit Werkzeug.
There is a heavy box with tools in the basement.