Gioco vs. partita
While both gioco and partita can be translated as game in English, they are not interchangeable. Gioco refers to the game as a concept, an activity, or a type, while partita refers to a single, specific match or instance of that game being played.
Gioco
A1This word refers to the general idea of a game, the rules, the activity of playing, or the equipment used to play. It's the abstract concept. It can also mean play in a broader sense, or a set of items.
Il mio gioco da tavolo preferito è Risiko.
(My favorite board game is Risk.)
Il gioco è un'attività importante per lo sviluppo dei bambini.
(Play is an important activity for children's development.)
L'allenatore ha studiato il gioco degli avversari.
(The coach studied the opponents' style of play.)
Ho ricevuto in regalo un gioco di scacchi in legno.
(I received a wooden chess set as a gift.)
Nel tennis, devi vincere sei giochi per vincere un set.
(In tennis, you have to win six games to win a set.)
Per un esperto, quel problema era un gioco da ragazzi.
(For an expert, that problem was child's play.)
Partita
A1This word describes a single, specific instance of a game being played from start to finish, especially in sports or card games. It is a match or a round. It can also have non-gaming meanings, such as a batch or consignment of goods.
Andiamo a vedere la partita di calcio allo stadio?
(Shall we go see the football match at the stadium?)
Ieri sera ho vinto una partita a poker con i miei amici.
(Last night I won a game of poker with my friends.)
La partita a scacchi tra i due campioni è durata cinque ore.
(The chess match between the two champions lasted for five hours.)
Il tennista ha vinto la partita in tre set.
(The tennis player won the match in three sets.)
L'azienda ha ricevuto una nuova partita di materie prime.
(The company received a new batch of raw materials.)
Per lui, la vita è una partita da vincere.
(For him, life is a game to be won.)
Summary
In essence, you play a partita (a match) of a gioco (a game). Gioco is the name of the activity itself (e.g., chess, football, tag), while partita is the specific event where you compete against someone (e.g., the 90-minute football match, the single round of chess you play against a friend).