For CMOS opamps, you are measuring GigaOhms for either, perhaps dominated by the leakage of ESD structures which degrades as temperature rises.
For bipolar, the common-mode at DC will be proportional to the stiffness of the tail current source of the input diffpair. For AC, the various capacitances affect that Zin.
For bipolar, the differential depends on beta * reac or beta * 1/gm, at DC
For bipolar at AC, the Miller effect will become a killer as the diffpair
moves into its linear region.
For example, examine datasheet of the UA715 opamp. Look at the schematic.
The input diffpair has "cascode" (common base) transistors before the load resistors. This reduces the Miller Multiplication to 2X or less.
Notice the emitter linearization resistor in the diffpair; these 2 resistors greatly expand the "linear response region" of the diffpair and allow a better control over Slewing region behavior, permitting faster settling.
What does this tell us? That the high_frequency differential input capacitance of OpAmps WILL VARY, determined by the region of operation.
The ESD protection structures/diodes may or may not dominate.
During Slewing, the input capacitance will be DIFFERENT from small_signal input capacitance.
