There are many different sports which use a ball. All would be considered a ball game; such as basketball, football, baseball etc. If you described one of them and said that you try to score by putting the bouncing ball through the goal posts, you would not know what you were talking about because there is no such ball game. The remark by your listener might be, "That must be a different ball game altogether." Now, you can apply the same reasoning to anything which is defined incorrectly. Eg., If I came to China and said, "It must be hot in China because the nation is so close to the equator." YOu would reply, "No, you must be thinking of Indonesia which is near the equator. China's climate is a different ball game altogether."