The images are data. Their classification is metadata
The terms data and information are often used interchangeably, but they do not have the same meaning.
For example, suppose your image data consists of pictures of dogs stored as JPEG files.
You can organize the files into directories, but the directories are simply labels that the file system associates with the data files. It is the human user that assigns meaning to the labels. The label is data. The meaning is information.
Biologists have long been great classifiers, and since a dog is an animal, the concepts of species and breed might be relevant. Your directory names might be the names of breeds. You don’t need to refer to this as “structural”, however. The “structure” has already been developed by dog breeders. The text “terrier” associated with a JPEG file (as its containing directory) is metadata. The information is the breed.
In fact, the Wikipedia articles on species and breeds are highly relevant to your question. Biologists are in general agreement about species. However, breeds exist within a species, and dog breeders disagree on the exact classification. Data is data, but information must exist in a human context.
Folders and directories exist in the grey area where data about data carries information, e.g. where “airedale” and “lakeland” might be subdirectories of “terrier”. However, their presentation on a screen is merely a convention. The “structure” is imposed from the outside. The directory labels are data that represents what dog breeders have decided to be useful information.
The relationship between data and information can also be approached through Korzybski’s famous aphorism: the map is not the terrain.