Banca d'Italia sits inside the Eurosystem, not outside it
Background
The capital of the European Central Bank comes from the national central banks of all EU Member States. Banca d'Italia appears in the ECB's own table of euro area national central banks, with a capital key of 13.0993 per cent and paid-up capital of 1,418,000,151.07 euro.
The ECB draws a line between two systems. The ESCB comprises the ECB and the national central banks (NCBs) of all EU Member States whether they have adopted the euro or not. The Eurosystem comprises the ECB and the NCBs of those countries that have adopted the euro. The Eurosystem and the ESCB will co-exist as long as there are EU Member States outside the euro area.
The euro area consists of the EU countries that have adopted the euro. The European Union's country page for Italy gives Italy's currency as the euro and records Italy as a member of the euro area since January 1999.
The primary objective of the ECB's monetary policy is to maintain price stability. The ECB's main decision-making body, the Governing Council, sets monetary policy for the euro area; it consists of six ECB Executive Board members and the Governors of euro area national central banks, who assess economic, monetary and financial developments before taking monetary policy decisions, every six weeks.
After the Governing Council makes monetary policy decisions, it is typically the national central banks which implement them - for example by lending money to commercial banks through refinancing operations. Banca d'Italia therefore takes part in the euro area decision and carries it out in Italy, rather than fixing an Italian policy interest rate of its own.
In plain words
Eurosystem — The European Central Bank together with the national central banks of the countries that have adopted the euro.
ESCB European System of Central Banks — The wider system: the European Central Bank plus every EU member's national central bank, euro user or not.
NCB National Central Bank — A member country's own central bank, as distinct from the European Central Bank.