Celery Soda is a traditional soda in the sense that it contains all the same ingredients, only varying slightly to provide the celery taste.
This Dr. Brown's Cel-Ray Soda contains carbonated water, high-fructose corn syrup, celery syrup, phosphoric and citric acids, caramel color, and natural flavoring.
In this instance, the natural flavoring is provided by celery seeds, among other flavors.