The color change you observe in apple butter versus applesauce is due to the difference in their cooking processes and the extent to which the sugars in the apples caramelize during cooking.
Apple Butter: Apple butter is made by slow-cooking apples for an extended period, typically several hours, until they break down, and their natural sugars caramelize. As the apples cook down, the sugars undergo a Maillard reaction, which is a chemical reaction between amino acids and reducing sugars that results in the browning of the food. This is the same reaction that occurs when you brown meat or toast bread.
The extended cooking time in apple butter allows the sugars in the apples to reach a high enough temperature to undergo this browning reaction, resulting in the rich brown color and deep, caramelized flavor characteristic of apple butter.
Applesauce: Applesauce, on the other hand, is usually cooked for a shorter period, just until the apples soften and break down into a sauce-like consistency. The shorter cooking time does not allow the sugars in the apples to undergo the same level of caramelization as in apple butter. As a result, applesauce retains the natural color of the apples used in the recipe, which is typically a light yellow or pale color.
In summary, the key difference between apple butter and applesauce lies in the cooking time and the extent of caramelization of the sugars. Apple butter is cooked for a long time, leading to significant caramelization and a rich brown color, while applesauce is cooked for a shorter duration, preserving the natural color of the apples.