4W measurements (Kelvin type) separate current and sense path.
That means that sense path is high impedance and measures voltage so any resistance (including contact resistance) has little influence.
On the other hand, as current source, 4W meters use constant current source, that will force certain constant current even if wiring and contact resistance in that current contour varies and is not stable. So you have stabilized current and separate voltage path.
Copper wires have quite high thermal coefficient. If you do 2W measurement by shorting wires, then measuring resistor, by the time you measure resistor things change... It is not stable.
4W measurement technique helps with measurements, compensates in changes and differences in cables etc etc... By the time you need to measure something below, say 10Ω, influence from cables is quite visible. Below 1Ω, influence form cables can be greater than DUT..
To put it colloquially, with 2W measurements your meter calibration is valid at multimeter sockets. With 4W calibration is (almost) valid (assuming correct good quality cabling and connection) at point of measurement, I.E at cable probes connected to DUT...
It is not exactly like that (metrology guys will kill me for this oversimplification) but it illustrates the difference.
4W purpose is to try to achieve that.