The primary difference between RAM (Random Access Memory) and ROM (Read-Only Memory) in computer systems is their purpose and volatility. RAM is a type of volatile memory, meaning it loses its data when the power is turned off and is primarily used for temporary storage of data and instructions that the CPU needs in real-time. In contrast, ROM is non-volatile memory that retains its data even when the power is turned off and is typically used for storing firmware and essential system instructions that boot up the computer.