You can create three different types of apps for Shopify stores: public, custom, and private. App types can't be changed after the app has been created.
A public Shopify app interacts with the Shopify API on behalf of multiple stores. All public apps need to go through Shopify’s review process. Apps that pass review are listed on the Shopify App Store by default. If you don't want your app to appear in the Shopify App Store search results or on category pages, then you can unlist it.
Learn about Public app authentication.
Custom Shopify apps interact with the Shopify API on behalf of a single store. The store's Shopify URL
example.myshopify.com is provided on app creation and can't be changed. Custom apps are not listed on the Shopify App Store and do not require a Shopify app review.
Learn about Custom app authentication.
Private apps interact with the Shopify API on behalf of a single store. Private apps are created in the Shopify admin, and are not listed on the Shopify App Store. Private apps do not require a Shopify app review.
Learn about Private app authentication.