Using cards as a metaphor can deliver many different kinds of play experiences, most of which have more in common with whatever original genre they're mimicking than other card games. A few examples:
The Collectible Card Game:
These games are typically heavily influenced by Magic: The Gathering and other cardboard imitators, with an emphasis on one-on-one multiplayer, draft formats, and discrete deckbuilding that ends before the match begins. This is probably the most central example that people think of when they think of a "card game," and it's the closest to being its own unique genre, but even so it's more of a subgenre within competitive turn-based strategy and tactics games. It has more in common with, say, Advance Wars, than it does with Slay the Spire. Speaking of...
The Dominion Clone:
These games are typically heavily inspired by the board game classic "dominion," involving roguelike elements, build-on-the-fly deckbuilding, and a mechanic where a certain pool of moves or cards gets exhausted and then reshuffled in the middle of battle. Again, it's more accurate to call this a turn-based strategy roguelike instead of a card game, per se, and it has at least as much in common with Dead Cells as it does with Magic.
The JRPG:
This kind of game really only uses cards as a metaphor for randomness within a traditional RPG structure. The attacks you'd normally select from a menu are instead represented by illustrated cards, but the card metaphor isn't operative on a gameplay level; it's just window-dressing.
But then again, that's true of basically every anything. I could retrofit almost any game that currently exists into being a card game with enough effort, particularly turn-based strategy games. Metal Gear Solid 5? All those soldiers you fultoned are cards! God of War? Your skill tree is cards! Death stranding? Each piece of cargo is a card!
Not only are card games not a genre, then, they're not even a gameplay mechanic. They're a skin you can layer on top of an existing design. They're a cosmetic coat of paint used to influence players' expectations and act as a short-hand for several other, more integral mechanics.
The Collectible Card Game:
These games are typically heavily influenced by Magic: The Gathering and other cardboard imitators, with an emphasis on one-on-one multiplayer, draft formats, and discrete deckbuilding that ends before the match begins. This is probably the most central example that people think of when they think of a "card game," and it's the closest to being its own unique genre, but even so it's more of a subgenre within competitive turn-based strategy and tactics games. It has more in common with, say, Advance Wars, than it does with Slay the Spire. Speaking of...
The Dominion Clone:
These games are typically heavily inspired by the board game classic "dominion," involving roguelike elements, build-on-the-fly deckbuilding, and a mechanic where a certain pool of moves or cards gets exhausted and then reshuffled in the middle of battle. Again, it's more accurate to call this a turn-based strategy roguelike instead of a card game, per se, and it has at least as much in common with Dead Cells as it does with Magic.
The JRPG:
This kind of game really only uses cards as a metaphor for randomness within a traditional RPG structure. The attacks you'd normally select from a menu are instead represented by illustrated cards, but the card metaphor isn't operative on a gameplay level; it's just window-dressing.
But then again, that's true of basically every anything. I could retrofit almost any game that currently exists into being a card game with enough effort, particularly turn-based strategy games. Metal Gear Solid 5? All those soldiers you fultoned are cards! God of War? Your skill tree is cards! Death stranding? Each piece of cargo is a card!
Not only are card games not a genre, then, they're not even a gameplay mechanic. They're a skin you can layer on top of an existing design. They're a cosmetic coat of paint used to influence players' expectations and act as a short-hand for several other, more integral mechanics.