Within the Biot poroelasticity theory, the effective pressure coefficient for the bulk volume of a fluid-saturated rock and the Biot coefficient are one and the same quantity. The effective pressure coefficient for the bulk volume is the change of confining pressure with respect to fluid-pressure changes when the bulk volume is held constant. The Biot coefficient is the fluid volume change induced by bulk volume changes in the drained condition. However, there is experimental evidence showing a difference between these two coefficients, arguably caused by microinhomogeneities, such as microcracks and other compliant pore-scale features. In these circumstances, we advocate using the generalized constitutive pressure equations recently developed by Sahay wherein the effective pressure coefficient and the Biot coefficient enter as distinct quantities. Therein, the difference is attributed to the porosity effective pressure coefficient that serves as a measure for the deviation from the Biot prediction and accounts for microinhomogeneities. We have concluded that these generalized constitutive pressure equations offer a meaningful alternative to model observed rock behavior.