Yes banks and wallets are different, Banks hold paper currency while wallets hold internet currency.
But when bitcoins will become so mature that they overrule all the currency and paper currency which bank holds have very little or low value, only then bitcoins will replace the Banks.
I don't believe that bitcoin can make the banks disappear. If there will be a chance that the paper currency will be low valued still they will not going to give up and they are connected to the government. Because they are trusted by the government and gov't will not going to take the chance of using bitcoin as our personal bank accounts.