Hi,
As I understood, you have all your files in the images/stories/slideshow folder. You are using these images in some articles and showing these articles in the JA Slideshow module. But you want to specify some description to each image and do not want to display text from related articles.
For that, you can simply use source as ‘From Image Folder’ in the module. With this you will need to specify the image folder from which images should be displayed and then for each image you can specify description as well as URL. For URL you can use the article link so that the image and description will ultimately take user to the corresponding article.
The syntax for specifying description and link for each image is
some description