The main difference is the technique: in a classic pedicure, the cuticle often stays half-done; in a Russian pedicure, the cuticle is fully cleaned. The nail plate looks longer, the skin is smooth, and the feet look neat even without color.
Besides, dry work lets the master see every detail. There is no swollen skin from water, and it lowers the risk of cuts and uneven work. For many clients, it means more comfort and better healing.