A "picture" is any kind of representation that is supposed to look like something real, as opposed to a "pattern" or a "design." An artist "paints a picture." You look at the picture, and you say "that is a horse." It might be a very realistic and precise picture, so you can tell the breed of the horse and see the hairs on the mane. It might be a stylized picture, just like an icon or a symbol. But you say "that is a horse."
"Picture" is an ordinary, everyday word.
A "photograph" was an image produced by a camera, on film. A photograph is a kind of picture. A photograph is always a very exact, precise, literal copy of what the camera sees.
"Photograph" and "photo" are ordinary, everyday words. Nowadays we often use the word "photograph" for "a picture made with a digital camera" even though film is no longer used.
An "image" means a picture, with an emphasis on exactness and precision. In physics, optics, and in the digital era it has come to mean an exact optical copy made by a lens, or a computer file that encodes such an image. "Image" is a somewhat technical word.
The lens of a camera also makes an image. It is not a photograph because it is not permanent. It is there only while the camera keeps pointing at a subject. A photograph is an image that has been made permanent.
Therefore: when a camera takes a picture, the lens forms an image. If there is film in the camera, the image exposes the film. When the film is processed and printed, you have a photograph.
I might say "I have a picture of my grandson in my wallet." (Excuse me, I'm not sure about Muslim culture; in Western culture it's considered perfectly acceptable to have pictures of people). I might also say "I have a photo of my grandson in my wallet." I would never say "I have an image of my grandson in my wallet."