Foams and sponges are soft by nature and generally specified for basic sealing applications. They are more flexible and malleable than solid rubbers of the same material.
Open cell foams have cells, or air spaces, which are interconnected and will thus allow the passage of liquids or gases. These types are not generally used for gaskets or seals. Closed cell foams where the cells do not interconnect are used for gasket and sealing purposes.