Each tag can be assigned to one or more tag groups, or it can remain unassigned. Tags that were created in the default tag box on the post edit screen or on the list of posts (via Quick Edit) are unassigned. If you create or edit a tag through the Tags page (in the Posts menu), you find there a pull-down menu with your tag groups.
Each tag can be assigned to one or more groups. These groups are then available for that tag when you edit a post. In each post you can still decide for which of these groups – one or more – you want to use that tag.
It is important to understand this difference: By assigning a tag to groups, you are only creating the options how this tag can be used in posts. For each post where this tag appears you can then choose among these groups. Only your selection in the posts determines
It is also possible to select multiple tags with the check boxes, select a tag group from the menu above and then click on “Apply”, in order to assign or unassign all selected tags together.
If you bulk-assign to a group, this group will be added to previously assigned groups. If you select “not assigned” for the bulk action, all groups will be removed from the selected tags.
On that “Tags” page you find a menu above the list that – once applied – shows only tags of a particular group, or only unassigned tags. If you don’t see that menu, you might have to enable it in the settings.