die Kabine
booth / changing room
A small, separate room used for a specific purpose, often for changing clothes.
Ich probiere die Hose kurz in der Kabine an.
I'll quickly try on the pants in the changing room.

cabin / booth
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booth / changing room
A small, separate room used for a specific purpose, often for changing clothes.
Ich probiere die Hose kurz in der Kabine an.
I'll quickly try on the pants in the changing room.

Pay attention to the case after the preposition 'in'. Use the accusative for movement ('in die Kabine gehen' — to go into the cabin/changing room) and the dative for a location ('in der Kabine sein' — to be in the cabin/changing room).
Der Spieler geht nach dem Training in die Kabine.
The player goes into the locker room after training.
The word 'Kabine' (cabin/booth) is often used in compound nouns to specify the type of cabin or booth. Examples are 'Umkleidekabine' (changing room), 'Fahrerkabine' (driver's cab), or 'Schiffskabine' (ship's cabin).
Die Umkleidekabinen im Schwimmbad waren alle besetzt.
The changing rooms at the swimming pool were all occupied.
The context makes clear what kind of 'Kabine' (cabin/booth) is meant. Words like 'anprobieren' (to try on) point to a shop, 'Schiff' (ship) to a trip, and 'Mannschaft' (team) to sports.
Auf der langen Fährfahrt hatten wir zum Glück eine eigene Kabine.
On the long ferry ride, luckily we had our own cabin.
In the context of clothing and shopping, 'Kabine' (changing room) is the standard term for the room where you try something on.
Entschuldigung, ist diese Kabine frei?
Excuse me, is this changing room free?
box
'die Box' and 'die Kabine' can both mean a separated area. However, 'Box' is often a special area for animals, equipment, races, or other specific purposes. 'Kabine' is used more for a small room that people use, for example to change clothes. Learners may confuse the words because both describe something separated off. If a person goes in briefly to change clothes or sit there, 'Kabine' is usually more natural. For a horse or a special service area, 'Box' is more likely to fit.

Im Schwimmbad zieht sich Lena in einer freien Kabine um.
At the swimming pool, Lena changes in a free changing room.
Vor dem Rennen fährt das Auto kurz in die Box.
Before the race, the car briefly drives into the pit.