The characteristic is already explained by the respective word. Waterproof shoes are really waterproof. This means that no water penetrates through the outer fabric. Most waterproof shoes are equipped with a waterproof membrane.
While there are fixed criteria with so-called water columns that determine the water permeability of a substance or a membrane, there are no fixed criteria for a water-repellent material.
Water-repellent means that the outer fabric repels moisture for a short time.