Finder tags
Finder tags are the coloured labels and named tags you give files and folders in Finder. A folder move between your Mac and your external drive keeps them.
Finder tags are the coloured labels — Red, Orange, Blue and so on — and named tags you give files and folders in Finder, so you can find related things together from the sidebar or a search.
A tag is stored as one of the file's extended attributes, not in its name or contents. So a copy that keeps extended attributes keeps tags; a copy that doesn't, loses them.
When Storage Studio moves a folder between your Mac and your external drive, each file's Finder tags go with it — including through a Relocate, where the tags travel with the file on the drive. Copies to a cloud account depend on what that provider can store, so don't rely on tags surviving there.
See also: What a move keeps · Extended attributes