Quantization noise and Quantization error
The quantization noise is an abstraction, meant to represent the quantization error as a signal (so it can be compared to other forms of noise.

You consider the quantization noise as the difference between the (real) quantized signal and the (ideal) sampled one. Because of the loss of information due to quantization, a signal that is A/D and then D/A converted will show an additional noise due to quantization.

A situation in which using quantization noise is useful is when determining the quantization depth (number of levels/bits) of a signal. By comparing the quantization noise to the other noise sources, it's possible to determine the maximum reasonable number of levels for the quantization, because additional bits would be absorbed by noise.

This of course happens if the sampling rule is respected.