What's the difference between a shunt resistor and a four-terminal resistor?
This is what I believe you mean: -



It's still a shunt resistor except there are bespoke pads for the measurement circuit. On very low ohmic value shunts this is usually compulsary for the better ones.

A 4 terminal resistor is usually a shunt resistor. But not all shunts have 4 terminals. This picture should explain why the errors are smaller when using bespoke terminals for voltage measurement to infer current: -