What is more accurate definition of Ohm's law?
If a circuit element is Ohmic, then the voltage across and current through are proportional

$$V \propto I $$

and the constant of proportionality is the resistance \$R\$

$$V = R \cdot I$$

This relationship, Ohm's Law, is obviously a linear relationship and thus the slope of the associated VI curve is just the constant of proportionality \$R\$

$$\frac{dV}{dI} = \frac{V}{I} = R $$

However, for a non-linear circuit element, e.g., \$V = R \cdot (I + \epsilon I^3)\$, the voltage across is not proportional to the current through and thus

$$\frac{V}{I} \ne \frac{dV}{dI}$$

Now we can define the terms static resistance and dynamic (or differential) resistance:

$$R_{static} = \frac{V}{I} $$

$$r_d = \frac{dV}{dI} $$

The static resistance is useful for DC analysis while the dynamic resistance is useful for small-signal analysis (where we linearize the circuit element about the DC operating point).

For more, see the Wikipedia article section static and differential resistance.