A graphic filter is a method that processes the pixels of a graphic object to produce a specific effect. For example, you can apply a blur filter to an object to make its edges appear softer, or you can apply a drop shadow filter to an object to make it appear with a shadow behind it.
A blend mode is a method of making the colors of a graphic object interact with the colors of other graphic objects beneath it. For example, by using the Lighten blend mode, you can make the parts of an object appear lighter in color to varying degrees depending on the colors of the objects beneath it.