Apparently there is two different things, Collections and Folders. Folders exist for personal vaults and collections for organizations. No idea why you can't use folders in organizations.
Yeah you're right. I think folders are more like a "tag" in that it's not actually a container (I think you can even put stuff from an Organization's collections in your personal folders).
Anyway, with Collections, you used to have to create a collection and enter the name as Some/Thing, to get a hierarchy going. But I think they improved that so that you can just create that hierarchy of collections int he web gui as if they were folders in folders.