The Magic Shop has 8 possible items available at a time and updates once daily. A Refresh Order can be use to change the items listed to a random other set of items. This is often used as an easy way to collect Fragments.
The Black Store works with the same mechanics as the Magic Shop, however only diamonds can be used to refresh the items and at VIP0 the Store is only open for a limited period. If you choose to increase your VIP level to VIP8 then a perk is available which allows the Black Store to always be open.