This is status-declined for reasons listed in answers below:
They are both well used tags, but they seemingly mean the same thing.
Which one should be a synonym of the other?
Webster defines it as
Definition of photo plural photos : photograph
photograph : a picture or likeness obtained by photography
Definition of photography : the art or process of producing images by the action of radiant energy and especially light on a sensitive surface (such as film or an optical sensor)
So no, it's not the same as a picture it has to be taken from a camera.
The saved file might still be considered a photo not an image.
A photo modified and saved in Photoshop would be considered a photo too