Three men are playing frisbee in the woods.
Three brothers are playing a friendly game of Frisbee before dinner.
In sentence one it doesn't specify that the 3 are brothers and it says they are playing in the woods so you wouldn't think they would be close to home for dinner.
Just because three men are playing a game does not mean they are brothers. One also cannot infer that the game was friendly or that it was before dinner.
Not all men are brothers, the game of frisbee may not be friendly, and they could be playing any time of the day before or after dinner.