If I take items from storage and put them back on the island will I get more prestige, or is that only..

When you take items out of storage you will not get prestige, you already collected prestige once. If you could get prestige for taking items out of storage there would be nothing to prevent you from putting items in storage, then taking them out and collecting again and again. Taking items out of storage allows to place items on your island again; you can leave them on the island, sell them for coins, or place them back in storage.