I will clarify the difference of the two definitions with an example. In the game Go (Go), the win condition is to earn the most points. To achieve this, a player must occupy the cell. So I define the game goal as a strategy, which the player needs to implement in order to win.
There are thousands of games, but only a small number of game objectives. Which means most games have the same objective. At first this may seem surprising. But when you look closely, since every game has winners and losers, the goal of the game should be something measurable, relatively simple, and expressed in the game.