If the waveform settles at the centre zero line, it’s asymmetric. If the waveform centre is above or below then it’s DC offset.
Looking at the OP’s waveforms it seems to be typical asymmetry.
From that SOS article -
In contrast, natural waveform asymmetry cannot be ‘corrected’ with a high-pass filter, and a rather more complicated solution is required called a ‘phase rotator’. Generally, there is no need to ‘correct’ a naturally asymmetrical signal, but occasionally the asymmetry can restrict how much the signal can be amplified because the stronger half of the waveform will reach the clip level before the weaker side. By using a phase rotator process to alter the harmonic phase relationships, a more balanced symmetry can be established, allowing slightly more gain to be applied before both sides reach the clipping level at the same amplitude. Asymmetrical waveforms can also sometimes confuse the side-chain level-detection circuitry (or algorithms) of some compressors, resulting in less effective compression than might be expected.
