UPDATE: As of 2021, ArcGIS content migration (such as items, groups, and users) from one organization to another is now transitioned from Admin Tools for ArcGIS to a more in-depth backup tool in Backup My Org.
Copy
The cool tool is an Admin Tools feature that creates a new item as a pointer to the original source, which is useful for multiple users that are all working on the same content.
Clone
The cloning tool is an exclusive Backup My Org feature that replicates existing ArcGIS items and creates new ones. With its hosted dependencies configured automatically, ArcGIS items are no longer pointing to the original data source it was cloned from. Cloning is a very useful tool ideally utilized for moving content from one ArcGIS organization to a new one. Backup My Org’s cloning feature offers an in-depth experience with configurable settings that help users clone ArcGIS content.