Since I suggested that anybody who is trying to define anything should check the definitions in a good dictionary, I decided to take my own advice. See the attached defs.htm for definitions of the words 'diagram' and 'structure' in the American Heritage Dictionary and the Merriam Webster Dictionary. In general, I have found the American Heritage definitions and etymologies very good. They are usually clearer and more precise than the definitions in other dictionaries. But it's always useful to get a second or third opinion.
An important distinction: A structure is a pattern in an entity of some kind. A diagram is a pattern that somebody draws or imagines as a representation or explanation of a pattern that somebody observed of found in some structure.
Therefore, a diagram would be more likely to be the kind of pattern that some human or animal or computer would be likely to use to support reasoning or computation about a pattern of any kind.
John