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A photo, short for photograph, is always taken with a camera.
A picture is the most general term for any representation of a person, an object or a landscape. It can be a painting or a pencil drawing, etc.
The delimitation of image and picture has its difficulties. "image" has an overlapping area with "picture" and it has uses of its own where "image" is preferred. For example.
God created Man in his own image. - Here the idea of likeness is expressed.
Firms are concerned about the image the public has of them. And they try to create a positive image by public relations.
The word "image" has a many-sided character and it is useful to have a look at a dictionary about special uses of image.
Personally, I don't see any difference between the two, but I can tell you that I recently found stock vector images. I needed to make a presentation for work and I found the baseball bat vector here on this site. I think that many people will find it interesting and useful, because there is a large selection of illustrations!
In US English, all these words may refer to a photo picture, in fact.
More strictly, picture is what an artists draws, photo is a short for photographm and this is what we take with a camera, and ai image can be mental, or drawn, or your outlook, or all of the above