The difference between puppy food and adult food isn't about digestibility really. Many puppy foods have the exact same ingredients as their adult versions. It's more that puppy formulas tend to have different ratios if the ingredients. Oftentimes puppy food will be higher in protein and fat than adult food. That makes sense because pups are growing muscle and tissue at a much higher rate than adults and they have a higher metabolism so they need the extra energy fats provide. Additionally, the ratio of calcium to phosphorus (which is key for proper bone growth) is typically different than that in adult foods. Lastly, some brands add things like DHL and DHP to promote healthy eyes and nervous system development. Again, because puppies are growing everything vs. adult dogs who are just maintaining.
Sometimes you see puppy food with ingredients that are "gentler" on the digestive system, but the primary reason for them being different from adult formulas is to provide a different nutrient profile marketed toward pups growing bodies.