The “Detailed Taxonomy Capabilities” area in PublishPress Capabilities is related to the Taxonomy-Specific Capabilities box, but goes one step further.
If you check the boxes shown below, you will see extra permissions for all your taxonomies:
This screenshot shows the default WordPress permissions for Categories and Tags:
This screenshow below shows all the extra permissions you will see thanks to “Detailed Taxonomy Capabilities'. You will now see that you can give “Manage”, “Edit” and “Assign” permissions for all your taxonomies.