Most of the LCR meters we're familiar with don't actually measure resistance, nor capacitance, nor inductance directly, they measure/set the voltage across the DUT and measure/set the current thru DUT. These measurements also includes the phase relationship between the DUT voltage and current for AC.
The DUT impedance is then calculated as vectors V/I, and for DC (no phase relationship) this is simply the DCR, and for everything else this is Impedance Magnitude Z with angle Theta. From here the Real and Imaginary Impedance R +-jX can be computed and then distilled into various additional displayed parameters using the measurement frequency and results in the familiar Cs + Rs, Cp +Rp, Ls +Rs, Lp + Rp and the related admittances.
Some handheld LCR meters such as the DE-5000 utilize a special chip-set that does most of the measurement and computational work with a few precision discrete components, however the bench type LCR meters like the Tonghui and Hioki we have, are more complex and precise, utilizing highly precision discrete components, various analog and digital chip sets and techniques, with high resolution/precision ADCs and various FPGAs, thus the additional measurement ranges and cost factors.
Best,