Hi,
the shortest weighting is based solely on distance, i.e., you get actually the shortest route.
The recommended weighting is mainly based on time, i.e., returns the quickest route (see the duration in your screen shots). Speed limits on smaller streets have a big impact on this. In addition, recommended may include some preferences for certain profiles, e.g., the bike profile prefers a bike-lane over a parallel street, even if it takes a bit longer.
Best regards,