The Italan equivalent of 401(k) is fondo pensione (retirement fund).
Italy, as well as a number of countries around the world, provides with public mandatory social security by INPS (*National Social Security Institute). Part of the employee's salary is paid to the INPS into a public retirement plan. Once the employee meets retirement criteria (mostly age, but also work disease and handicaps may apply) the employee goes into retirement and is paid a lifetime money.
We won't go into computation details, but if you are subscribed to INPS you can simulate your future retirement pension.
As an alternative, salaried employees MAY subscribe to a private fondo pensione run by insurance companies. It is interesting that employees may opt in for investing part of their TFR (trattamento di fine rapporto, termination indemnity) into the fund, thus increasing their retirement pension.
Autonomous workers are obligated to pay INPS contributions, which in the present time serve to pay retirement pensions to the existing retired.
A saving account is a conto deposito, offered by most banks, where customer locks an amount of money of their choice for a minimum time in exchange of an interest rate that is higher to the normal active interest rate of checking accounts.