I answered earlier to OP directly at top-level comment, but I want to answer this one directly. The impulse response is the same thing as the frequency response, it is just time-domain characterization of the system, whereas frequency response is the frequency domain equivalent, though we are usually not shown the complex number nature of the frequency spectrum where phase information of the sound is encoded because we do not hear phase directly and the phase plot doesn't relate to anything we can intuitively understand.

If the speaker membrane moves slowly back to neutral position after an impulse has excited it, that would show up as a decaying plot, and in frequency response would look like a low-pass filter. One way to understand it is to think that system isn't fast enough to reproduce waveform that cycles in and out of phase within that decay region, so if the wavelength is short relative to the impulse's decay time, it cancels with prior versions of itself that are decaying in the impulse, resulting in little output.

In this case, the impulse drops gradually rather than instantly, suggesting that there is some low-pass filtering effect, but also overshoots and goes below zero, which suggest to me that it has could have high pass filtering characteristic, too. For low frequencies, whose wavelength is long relative to the impulse, the negative parts of the impulse subtract from the positive side, and reduce output for low frequency. The fact impulse also returns to the positive side suggests it also contains a resonating component, though. If wavelength is the same as the impulse's ringing around zero level, then it will be amplified by the impulse response.

Finally, if impulse response is ideal, and system's frequency response is perfectly flat, and phase is linear, the entire impulse response is just a single spike with perfect silence surrounding it forever. The ideal impulse indicates that whatever the signal wants to do, the system can reproduce without altering it.