Literally, toy refers to something for a child to play with or something paltry or trifling, while, game refers to some activity engaged in for diversion or amusement. The common character of toy and game is that they are fun and amuzing. Toy often reperents some real objects for playing, i.e. the doll, toy bricks, and the game consoles. The concept of game is more general and abstract. Any activity that is neither mandatory nor a job and you feel fun in doing it can be regarded as a game. If you like Super Mario, that is a game. If you enjoy roller skating, that is a game. If you are crazy about programming, coding is a game for you.
Furthermore, the game activities require the players be active. You enjoy sitting near Lake Michigon and watching the sunset, it is fun and leisure but generally not viewed as a game. On the other hand, the toys are usually passive. They are waiting quietly for the players. In a word, playing toys is a game, real objects in games are toys.