What term is most appropriate for a high gain, direct-coupled differential amplifier whose characteristics are determined by components mounted externally?

An operational amplifier (op-amp) is classically defined as a high-gain, direct-coupled differential amplifier. The term 'operational' stems from its historical use in analog computers to perform mathematical operations like addition, subtraction, and integration. The defining feature of an op-amp is that its internal open-loop gain is exceedingly high, meaning its actual real-world performance is almost entirely dictated by the external feedback components (resistors and capacitors) chosen by the designer. While summing and difference amplifiers are specific configurations built using op-amps, the component itself is the operational amplifier.