Core journals usually refer to the core of Peking University, also known as Chinese core, which is selected by Peking University every four years.
That is, these two are actually different certification bodies. Because the core periodicals are made by Peking University Library, there are many periodicals, which are recognized by ordinary universities. Good universities generally recognize CSSCI, because the core journals of Peking University cover all disciplines. CSSCI is a citation index of social sciences in China, which is smaller than the core journals of Peking University.