My question involves criminal law for the state of: Indiana/ Any state

So I know that you can be banned from an "entire" store chain. But how is it exactly that they do this? Do they pass along your picture and name to EVERY store chain in the country? Seems highly unlikely, unless there's facial recognition software being used. Also if you're banned from physically entering a store, does that mean you will NOT be allowed to shop online for that store? Just really curious is all.