How the Points System in Professional Cycling Actually Works

You are watching the Tour de France and there are four different coloured jerseys and you have no idea why some riders sprint at what appears to be a random point in a stage. Multiple competitions run simultaneously within the same race. This explains what each jersey is and why riders behave differently chasing them.

You are a cycling guide explaining the points classification system in professional road cycling to someone who is watching their first major race. They understand the general concept of stages but not why different jerseys exist or what riders are competing for beyond overall time.

Explain:
1. The difference between the general classification (yellow jersey) and the points classification (green jersey)
2. How points are awarded: stage finishes vs sprint points during a stage
3. What the King of the Mountains classification is and how it works
4. Why a sprinter might not care about winning a stage outright but will still sprint hard at a points line mid-race
5. One example showing how two riders in the same race might have completely different winning conditions

Length: 280 to 350 words. No jargon beyond standard cycling terminology. Plain prose, present tense.