It says in the Wiki that both the Piggy Bank and Safe can be used as an extension of storage, but having multiple of the same thing only accesses the same items.
Question: Do Piggy Banks and Safes access the same 20 items? Or are the Safe's 20 items separate from the Piggy Bank's 20 items?
(That is, will having both increase one's inventory by 20+20=40 slots, or only by 20 slots?)
No. Safes and Piggy Banks are separate storage.
They are separate storage.
The advantage of a safe is that it can be placed anywhere, and the piggy bank needs to be on a table/other furniture. Piggy bank is therefore more suitable for storing coins, and valuables.
I would recommend using the safe for things, you may need while mining, or exploring the world. I often keep the safe in my inventory, and keep e.g. bombs, less important but useful potions in it, and when I need them anywhere in the world, I just put down the safe, pick up the things I need and then hammer it right back to my inventory.
