What is the difference in banking terms between "cuentas" and "cuentas claras"? The latter seems to be a service for which the bank charges a fee.
Cuentas would be any kind of bank account.
Cuentas claras must be a specific product from a certain bank. "Cuentas claras" is nothing like a "Cuenta de ahorro (Savings account)" o "Cuenta corriente (Checking account)", which are the main kinds of accounts for any bank.
For example, the bank ING Direct has a "Cuenta Naranja" which is nothing but the name they have given to a (savings) account with specifics conditions. They are the only bank that has "cuentas naranja".
In addition the expression "tener las cuentas claras" just means that the numbers are easy to understand (they are "crystal clear").