People tend to use the inertia H constant (MW*s/MVA) when it comes to describing the amount of inertia that grid forming inverters and batteries can provide. Sometimes the units are simplified to seconds, which makes it easier to understand how many seconds it could provide rated power for this specific function.
Active inertia or synthetic inertia do vary power when frequency changes but the key is the dynamic behavior. They typically do so by emulating a synchronous machine by implementing something like the swing equation in the active power control (see REGFM_B1 [1]). They essentially emulate the inertia, which makes them have some damping in changing the phase angle and frequency of their voltage waveform just like a spinning synchronous generator would when resisting frequency changes due to physical inertia, resulting in an inertial active power response. This makes it easier for people to analyze because they understand the swing equation from synchronous generators.