Note: This is about the UI, there is also a page about Capacity and Function.

Inventory (UI)

1LevelLevel beside the Badge is only shown when it is a painted user badge
2Producer
3RatingOnly shown on painted user badges
4Type in InventoryNumber depends on chosen Filter. The + means that this badge type is already in your chest. A - means that no badge of this type is in your chest yet.
5BadgeID
6Creation Time
7(special) NameMostly on System-Badges
8ChestIf you select all as filter, this shown that this badge is located in chest
9Droppeddid you already dropped this badge?
Short tap on badge typeopen/close badge list of this type
Long press on badge typeopen user Profile, not working on System/skill
Short tap on badgebadge detailled view
Long press on badgeprecise drop, works even in chest

You can sort each filter by Producer, Level, Quantity, Beauty-Rating and TypID.

Bag

This is you main and default inventory.

Chest

This is your storage vault. It prevents you to accidently drop badges. Put all badges here, which you are not planning to drop in near future, this keeps your bag handier.

Own

New

NPB

This filter shown only the non player badges (aka system, skill, ruler, explorer, mapper and so on)

Art

Show only painted badges.

All

Show all Badges in Inventory. Badges marked with an “+” (see number 8 on this picture) are located in Chest, Badges without “+” in Bag.