i presume During the digital-to-analogue conversion process, each sampled value is converted to its closest quantisation value.

Does anyone have different thought, please explain?

one does not sample digital data. The code for the value in digital code is converted to analogue, the method of conversion can vary.

Now in analogue to digital, the analogue is sampled, and that velue is converted to a digitial value which is near the value of the sample.