A core banking system is the software platform at the centre of a bank's operations, described in full in the main entry on core banking. It keeps customer accounts, posts deposits, withdrawals and transfers, calculates interest and fees, and maintains the records that feed the bank's general ledger.
The two terms are often used interchangeably. Strictly, "core banking" can refer to the set of central services a bank provides across its branches and channels, while "core banking system" refers to the specific software, whether bought from a vendor, built in-house or used as a cloud service. Systems typically include a deposit ledger, loan modules, product configuration and interfaces to card processors, payment rails and digital banking apps.
Replacing a core banking system is one of the largest projects a bank can undertake, because almost every other system depends on it. Many newer banks and Banking-as-a-Service providers use modern, API-based cores designed for rapid product launches.