Difference between "|Z|" and "Resistance" in capacitor datasheet?

One graph says it is displaying |Z|, whereas the other graph says it's displaying "R". Obviously the 2 graphs are different,

Impedance (\$Z\$) has both resistive and reactive components:

$$Z = R+jX$$

So if the ESR is small compared to the reactance of the capacitor (as it should be, especially for low frequencies) then \$\left|Z\right|\$ has almost nothing to do with ESR, and almost everything to do with \$jX_c = \frac{1}{j\omega C}\$.

At high frequencies, although it isn't a desirable characteristic, the inductive reactance of the part tends to dominate \$Z\$, and again the ESR becomes mostly irrelevant to determining \$\left|Z\right|\$.

but what's the meaning of the second one? Is it ESR?

Yes, the second curve is giving ESR. This is important in many applications, because even though it doesn't much affect the behavior of the circuit, it does affect how much the capacitor self heats, as well as the Q factor of any resonator using the capacitor as a component.

but what's the meaning of the second one? Is it ESR?

It's a combination of ESR and dielectric losses lumped together and computed as a series resistance to the capacitor. So, at 100 Hz the capacitive reactance is around 160 kOhms and the series loss resistor is around 700 ohms i.e. a Q of around 230.

At 100 kHz Q has dropped to around 100 and keeps falling until self resonance is arrived at and, beyond the SRF, the capacitor is inductive.

Searching internet on the terms: "murata capacitor impedance resistance" gives me as first hit:

https://www.murata.com/en-eu/products/emiconfun/capacitor/2013/02/14/en-20130214-p1

Today's column describes frequency characteristics of the amount of impedance |Z| and equivalent series resistance (ESR) in capacitors.
Understanding frequency characteristics of capacitors enables you to determine, for example, the noise suppression capabilities or the voltage fluctuation control capabilities of a power supply line. Frequency characteristics are therefore important parameters that are essential for circuit design. This column describes two types of frequency characteristics: impedance |Z| and ESR.
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ESR also shows frequency characteristics for values equivalent to loss.

Likewise, the datasheet also gives impedance |Z| and ESR