The two are distinct. Though 사진 is often translated to English as "picture", it is more literally 'photograph'. 그림 on the other hand is a drawing, painting, something hand made. If you use the 어학사전 on naver, bother 그림 and 사진 show translations for the words as "picture," but there is really very little overlap in the meaning.
I ran into an interesting example of this several days ago. While working with a group of Korean university students during a program orientation in the US (so we were working in English), they were tasked to draw pictures of pigs and then stated that the method in which they drew the pig was informative about their general personality (just a fun activity, not serious). Afterwords, I had my drawing of a pig and I asked one of the students "Would you like a picture of a pig?" (offering my drawing to her jokingly) so she hesitated momentarily, and said "Okay," got out her phone and took a photo of the drawing of the pig.
The mistake began with me using the word picture, which she translated to '사진'. Because of this she thinks I asked he if she would like a photograph of the picture rather than the drawing itself.