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Juego vs. juguete

While both juego and juguete are related to the concept of playing, they are not synonyms. Juego refers to a game or the act of playing, while juguete refers to a physical toy.

Juego

A1
The word juego refers to the activity, sport, or concept of a game. It is the action or the rules of play, not a physical object.
Mi juego de mesa favorito es el Monopoly.
(My favorite board game is Monopoly.)
El juego de las escondidas es divertido para los niños.
(The game of hide-and-seek is fun for children.)
Compré un nuevo juego para la consola de video.
(I bought a new game for the video game console.)
El juego de fútbol empieza a las ocho de la noche.
(The soccer game starts at eight at night.)
Necesito un juego nuevo de sábanas para la cama.
(I need a new set of sheets for the bed.)
Los juegos de azar pueden ser muy adictivos.
(Games of chance can be very addictive.)

Juguete

A1
The word juguete refers to a toy, which is a physical, tangible object specifically designed to be played with.
El niño guardó todos sus juguetes en la caja.
(The child put all his toys in the box.)
Mi juguete preferido cuando era pequeño era un tren de madera.
(My favorite toy when I was little was a wooden train.)
La tienda tiene una sección entera de juguetes para bebés.
(The store has an entire section of toys for babies.)
Para Navidad, ella pidió una muñeca de juguete.
(For Christmas, she asked for a toy doll.)
El perro destrozó su juguete de plástico.
(The dog destroyed its plastic toy.)
No me gusta pisar un juguete por accidente en la oscuridad.
(I don't like to accidentally step on a toy in the dark.)

Summary

In short, the key difference is that a juego is an intangible activity or game (the action), whereas a juguete is a tangible, physical object used for play (the item). You use a juguete (toy) to participate in a juego (game).