Multiply Multiplies the Image color and the Brush color. The result is darker. Painting with Black will produce black, painting with white will leave the Image colors unchanged. All colors in between will darken the image. Difference Subtract the Image Color from the Brush color or Brush color from the Image color, whichever is brighter.
Screen Works the opposite way of Multiply.
The result is lighter. Painting with black will leave the Image unchanged, painting with white will produce white. All the colors in between will lighten the image. Here is the sample of basic modes. What it does, is it using Multiply or Screen depending on the brightness of the Image color.