Clipping is the extreme form of limiting. When a transient goes through a slow limiter, it is softened, because its level is dropped so much. But when it is clipped, you get the maximal possible RMS and thus the transient stays relatively sharp. I don’t think it has much to do with extra ringing after the DAC.
Good limiters know when to clip a transient, based on its spectral content, and when to switch to slower release times to avoid distorting the sustained loud signals.