Read-Only Memory (ROM) and Random Access Memory (RAM) serve different purposes in a computer system. ROM is non-volatile memory used to store firmware or software that rarely changes, such as the BIOS, and retains its data even when the power is off. It is generally slower and not designed for frequent read/write operations. In contrast, RAM is volatile memory used as the main memory for storing data that the CPU needs to access quickly. It loses all data when the power is off but allows for fast and frequent read/write operations, making it essential for running applications and processing tasks efficiently.