The URL has not been "generated" in the same sense. You are retrieving an existing string. The images from google are not "generated" in the same sense, they are indexed from google's search algorithm.
The generative models, specifically for DALLE here, compute pixel unique images. You might say these models index a subset of an extremely high dimensional space (pixel count * RGB color values) using a query. Traditional search engines build an index from nothing and then use a search query to find the best matches in a more discrete space.
