Competitive Solitaire Games
These games are based on the single player traditional solitaire games, but add a competitive element by playing with one or more opponents. These opponents could be playing a completely separate game of solitaire on their own (Simultaneous Solitaire) but more often players are allowed to play on each other's cards or there is a shared (part of the) layout. The most well known example is Spite and Malice (also known as Cat and Mouse) but there are others like Crapette (Russian Bank) or Spit (Speed).
Trick Taking Games
These games have multiple players which each have a hand of cards. Every round (or trick) each player plays one card. Game-specific rules determine which cards are allowed to be played and which card wins a trick. In plain-trick games, the objective evolves around the number of tricks won (e.g. the game Spades), while in point-trick games the rank of the cards in taken tricks determines who wins or loses (e.g. the game Hearts).
Hand Comparison Games
These games typically don’t involve playing cards. Instead players are dealt cards at the beginning, and additional cards can be turned or dealt, extra cards could be drawn, or cards could be rearranged. When playing against the bank instead of against each other, these games are called banking games (e.g. Blackjack). When players raise stakes before showing their cards, these games are called vying games (e.g. Poker).
Card Exchange Games
These games have multiple players which each have a hand of cards and try to collect certain cards or a certain combination of cards. Players exchange one or multiple cards in a move, either with other players or with a stock of cards. The exchange of cards can either happen by drawing a new card and discarding a card (e.g. Rummy, Gin Rummy, or Stop The Bus) or by asking other players for a certain card (e.g. [Go Fish][go-fish]).