Extended attributes
Extended attributes are small pieces of extra information attached to a file, such as its Finder tags or where it was downloaded from. Folder moves keep them.
Extended attributes are small pieces of extra information attached to a file, kept alongside its contents. You rarely see them directly, but you see what they do: a file's Finder tags, the note of which website a download came from, and the check macOS runs the first time you open an app you downloaded all rely on them.
When Storage Studio moves a folder between your Mac and your external drive, extended attributes are copied along with each file.
Copies to a cloud account usually keep less, because each provider stores only some of a file's extra information. A drive formatted as exFAT can also behave differently from a Mac-formatted one.
See also: What a move keeps · Moving folders safely