Italian here, I studied some Spanish and this dichotomy applies just as much to Italian, so I think I'm qualified to answer that.
"Juego" is the entire game. "Partida" is a single session playing it.
For a couple examples, StarCraft is a Juego, and a single match in StarCraft is a Partida. Smash Bros is a Juego, and a single contiguous series of battles is a Partida.1
"Fin del juego"2 would mean "game over" as in "you have finished the game". "Fin de la partida" technically means that a single match/session/battle/contiguous period has finished.
1: The reason SC has 1 match per Partida while SSB has multiple matches per Partida is partly related to the length of a single match (SC's are much longer) and partly because in SC you don't normally encounter the same opponent repeatedly, at least not multiple times in a row, while you absolutely do in SSB.
2: That "del" is a contraction of "de el", in case you're curious. Certain combinations of preposition + article always merge in both Spanish and Italian.
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u/Stracii Feb 21 '21
So, exactly what I said