The question that you linked already talked about the difference between them. You're just asking which best applies to digital pictures? Well, one of them is already in the name of the thing you're talking about and it isn't image.
Going by their OED entries, any visual representation whatsoever is a picture, an image should properly represent something, and a photograph should properly be an image created by actual light reflected off an actual surface and captured by some machine or chemical process.
The Venn diagram would be a series of concentric circles: every photograph is an image but not all images are photographs, every image is a picture but not every picture is an image.
People don't really know that (see @stangdon above) and consider image to be more latinate and therefore prestigious. "Picture" makes people vaguely think of third-grade art class. You're in a business, so don't bother disabusing them of their mistake. Just use image and sound professional like everyone else, until it becomes come enough that picture goes back to being the prestige word.