Your Pockets are your standard carry slots. The slots here will not be affected by any type of Bag you have (or do not have) equipped. Currently, there is no way to expand your Pockets section.
Your Bag area contains additional carry slots. This can be unlocked through equipping different types of Bags. The higher quality the Bag, the more slots you unlock.
If you die, you will lose the Bag you had equipped and you must track down your body to loot it back (along with all of your carried Items and equipment).