Picture and photo overlap in meanings.
Editor Emily Brewster explores the similarities and differences between the two words:
Picture is certainly the broader of the terms. Unless the context specifies, picture can apply to a painting, drawing, or photograph. When followed by the word of, picture generally refers to a photograph. I would guess that this is the kind of picture most people think of if they hear picture out of context:
I need to have a new passport picture taken.
She showed me a picture of her parents.
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Photo is synonymous with photograph. It does not apply to paintings or drawings; it only applies to images made through photography.
I need a new passport photo.
When will we see your vacation photos?