They are similar. The meanings overlap. I'm going to describe the main meanings.
"Pic" is informal and short for "picture." (Similarly, "photo" is short for "photograph.")
"Picture" can mean a drawing, a photograph, or anything that looks like ("depicts") something real. "The child's book is full of pictures." "A picture hung on the wall--a copy of one of Diego Rivera's frescoes."
"Image" suggests something that is absolutely precise, realistic, and possibly produced by an optical system rather than an artist's hand. The lens of the eye forms an image on the retina; the lens of a camera forms an image on the film. The image may not be permanent. "This camera lens produces a sharp image." In computer graphics, "image" suggests a file format consisting of millions of pixels, mapping an image point by point--as contrasted with "vector graphics."
Before digital imaging, the word "photograph," from roots meaning "write" and "light," always meant a permanent image on a piece of film, or printed onto photographic paper. Thus it was a highly detailed, literal image of a real scene. (For decades, artists and photographers argued about whether photography could be an art form). Nowadays, we still call images, taken with digital cameras, and printed on pieces of paper, "photographs."
In the late 1800s, the technology known as "cinema," "movies," "motion pictures," or "moving pictures" was developed. These were "pictures" that "moved," so it became necessary to distinguish "still pictures" from "moving pictures." However, when it is clear from context, "moving pictures" can be called simply "pictures." A movie theater can be "a picture show." The movie industry can be "the pictures."