Face wash is usually formulated to remove daily pollutants and dirt. However, they are not formulated to remove makeup the same way that face cleanser does. A face wash tends to be more hydrating, whereas a skin cleanser tends to remove both pollutants and oils, while penetrating deeper into your pores.
Face cleanser also comes in multiple formulas - gel, foam, oil, cream, or water. This helps you choose a skin cleanser that suits your skin type or target area.
Keep in mind how often you use skin cleanser. Over cleansing can strip your skin of natural oils that protect your face, especially if you have dry skin. The best makeup remover for dry skin is also formulated as a gentle skin cleanser. This way, you do not have to use too much cleanser on your skin.