Kelvin type connection
The diagram is really confusing. In the 4-wire connection below on the right, for resistance measurement, the "force" wires are the ones (with red arrows) providing the current for the resistor under test. Through the "sense" wires only the current required by the voltmeter is circulating, causing a much lower drop.



In this example both current and voltage are being measured but the voltage source and current measurement could be replaced by a known current source. With the circuit on the left when you calculate the resistance from the current and voltage values you are actually calculating the resistance of the probe wires added to the DUT.

Regarding the "force voltage" "measure current" you mention, imagine if on the circuit on the left you didn't have the voltmeter. You would measure the current passing through the DUT, but the known voltage would be applied to the series association of the DUT, probe wires and the current meter. This would make the error even worse.