Why is there this difference? There’s no secret agreement. When the currency union was founded governments decided to transfer functions and tasks that are necessary for monetary policy to the Eurosystem and to leave other tasks as the responsibility of the national central banks. They invest, for instance, to cover the pensions of their employees or to build up capital and reserves.
Some central banks also manage the investment portfolios of other central banks outside the euro area and invest this money so that it stays in circulation. It’s vital that the Governing Council of the ECB is in full control of the size of the Eurosystem balance sheet, and that is the case. If that’s the case, why not do it publicly?