"Picture" is the more generic term, and includes any kind of visual representation, whether it is drawn, painted, photographed or produced by some other means. You could even call a naturally produced image a "picture". The word picture can even refer to a memory or mental process that is by nature completely immaterial.

"Photograph" virtually always refers to a physical image created with chemical or digital imaging technology.

Even though it's wrong to say " Let's take a picture " many people still say it. A picture is something you could draw or paint. while a photo is something that you take with your camera.