снимок is a image or print of something. It can be a photo, X-ray or any other medical image, image made from space etc. фотография refers only to a photo or the art of photography in general

Actually there is no special difference , if to say about pictures . But by the word фотография we can point all issue referring to profession , making photo , chemical process of it ... by word снимок -it is impossible. Я зарабатываю фотографией- i earn money by photography ( to say truth- i do it actually) . Я делаю снимки - i make pics. Мне понравилась фотография - i like the photography - here i can refers to a concrete pic. or to all issue of photography , depending from context. Мне понрафился снимок - it is always to a concrete pic. also as photographer slang i can say about a photo pic- отпечаток , картинка , карточка. фотка ( most common slang between non-professional )

фотография comes from the root фото (photo) снимок comes from the word снять (take off), we use it instead of "shoot"