There are two ways to access a tree. Either by its long url, or its short url. So either of the following work.
That is because group is both a usual folder, and it is a branch object, it has an index to all of its leaves.
Accordingly there can only be 1 copy of any name (object id), under a branch of the tree. Group Root Categories are branches. Private Root Categories are also branches.
It should also be noted that object ids are unique within a branch.