
die Decke
blanket
A large piece of fabric used to cover oneself and keep warm, usually in bed or on the sofa.
Weil mir kalt war, habe ich mir eine zusätzliche Decke geholt.
Because I was cold, I got myself an extra blanket.
blanket / ceiling
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blanket
A large piece of fabric used to cover oneself and keep warm, usually in bed or on the sofa.
Weil mir kalt war, habe ich mir eine zusätzliche Decke geholt.
Because I was cold, I got myself an extra blanket.

ceiling
The upper, inner surface of a room that closes the room off at the top.
Die Lampe hängt direkt über dem Tisch an der Decke.
The lamp is hanging from the ceiling directly above the table.

covering / layer
A layer that covers something, for example a tablecloth on a table or a layer of snow on the ground.
Am Morgen lag eine dünne Schneedecke auf den Autos.
In the morning, there was a thin layer of snow on the cars.
All meanings of 'Decke' (blanket/ceiling/covering) are derived from the verb 'decken' (to cover). A blanket warms you by covering you; the ceiling covers the room from above; a layer of snow covers the ground.
Die Wolkendecke war heute sehr dicht.
The cloud cover was very dense today.
The preposition helps identify the meaning. When talking about the ceiling of a room, you say 'an der Decke' (on the ceiling). When talking about a bed blanket, you say 'unter der Decke' (under the blanket).
Die Spinne krabbelt an der Decke.
The spider is crawling on the ceiling.
The idiom 'jemandem fällt die Decke auf den Kopf' literally means 'the ceiling is falling on someone's head' and means that someone is bored or restless at home and urgently needs to get out.
Nach drei Tagen Regenwetter fällt mir langsam die Decke auf den Kopf.
After three days of rainy weather, I'm slowly starting to feel trapped at home.
When referring to a warming blanket, typical verbs are 'sich zudecken' (to cover oneself up), 'sich in eine Decke kuscheln' (to snuggle into a blanket), or 'eine Decke umlegen' (to wrap a blanket around oneself).
Er kuschelte sich mit einem Buch und einer warmen Decke aufs Sofa.
He curled up on the sofa with a book and a warm blanket.
In the meaning of 'Schicht' (layer), 'Decke' is often used as the second part of compound nouns, for example 'Schneedecke' (snow cover), 'Wolkendecke' (cloud cover), or 'Staubdecke' (layer of dust).
Über den Bergen hing eine dichte Wolkendecke.
A dense layer of cloud hung over the mountains.
duvet / comforter
A Decke can be used in bed, on the sofa, or elsewhere to keep someone warm. A Bettdecke, on the other hand, is specifically intended to cover someone in bed. In the context of a bed, both words are possible, but Bettdecke is more precise.

Für die Nacht legte sie eine warme Decke auf das Gästebett.
For the night, she placed a warm blanket on the guest bed.
Für die Nacht legte sie die frisch bezogene Bettdecke auf das Gästebett.
For the night, she placed the freshly covered duvet on the guest bed.