A picture is defined as "a painting or a drawing", with no other noun defintiondefinition (although one of the sub-definitions is "the image on a television screen"). Meanwhile an image is just "a representation of the external form of a person or thing."
Basically, an image can be a photograph, a painting, or a drawing (or even an optical appearance like in a mirror, lens, or hologram), but a picture can only be a painting or a drawing.