Listed Public Apps
Each and every public app that passes through the extensive approval process of Shopify possesses a profile page on the Shopify App Store.
These apps are mainly built for developers creating an app customized for a single trader. Easily installable from Shopify Store, they do not require to pass through any approval procedure.
These apps are authenticated to interact with Shopify APIs and are not connected in the Shopify admin. these apps cannot use the app extensions
Unlisted Public Apps
Unlike the listed ones, these public apps do have a profile page on the Shopify App Store. Depending on the nature, type or model of the business, you can choose if you want to keep it listed or unlisted.
Such apps are meant for private developers creating an app for a particular business with certain typical requirements not fulfilled by custom apps. These are created for a one Shopify store or a small group of clients.
These apps have their individual infrastructure but reflect directly in the Shopify admin or frame. Eligible to use Shopify app Bridge, they can access app extensions.