das Kartenspiel
card game
A game played with a set of playing cards according to specific rules.
Am Abend saßen wir zusammen und spielten ein lustiges Kartenspiel.
In the evening, we sat together and played a fun card game.

card game / deck
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card game
A game played with a set of playing cards according to specific rules.
Am Abend saßen wir zusammen und spielten ein lustiges Kartenspiel.
In the evening, we sat together and played a fun card game.

The word is composed of 'Karte' (card; plural: Karten) and 'Spiel' (game). So it literally describes a game that you play with cards.
Lass uns heute Abend ein Kartenspiel ausprobieren.
Let's try out a card game tonight.
The verb in the sentence helps you understand which meaning is intended. The verb 'spielen' (to play) refers to the activity, while verbs like 'kaufen' (to buy), 'mischen' (to shuffle), or 'haben' (to have) refer to the deck of cards.
Wir haben bis spät in die Nacht Kartenspiele gespielt.
We played card games until late into the night.
When referring to the activity, the phrases 'ein Kartenspiel machen' (to have/play a card game) or 'ein Kartenspiel spielen' (to play a card game) are often used. You can also 'gewinnen' (win) or 'verlieren' (lose) at a card game.
Wer macht beim nächsten Kartenspiel mit?
Who wants to join the next card game?
deck
'das Deck' and 'das Kartenspiel' can both mean a set of playing cards. In this sense, they are very similar: you can shuffle a 'Deck' or a 'Kartenspiel'. However, 'das Kartenspiel' can also mean the game itself, that is, the rules and the act of playing. In this relation, 'das Deck' refers only to the cards as a set. Learners may confuse the words because 'Kartenspiel' has two meanings. If you mean the cards in your hand, both often fit; if you are talking about playing or the rules, 'Kartenspiel' is more natural.

Am Abend lernen wir ein einfaches Kartenspiel.
In the evening, we learn a simple card game.
Mein Bruder nimmt ein neues Deck mit in den Urlaub.
My brother is taking a new deck with him on vacation.