The 2nd version or "full store" includes the crafting and reward tabs, which aren't available from the pause menu. Seems pretty obvious to me.
This is essentially it. Because navigating tabs within tabs isn't really possible, the featured store entry point in the pause menu opens (on any interaction in that screen) the store UI, which has tabs for crafting and rewards.
Prospero is a shortcut to the featured store and (I can't recall her name) is a shortcut to the crafting store.
Definitely opportunities to improve this oddness, but not at the top of the list currently.