If the cervical discs have reduced height, would these be classed as compression fractures? if not, what else would they be classed as?

No: Loss of disk height is due to disk degeneration. Compression fractures are breaks in the main part of the bone (vertebral body).

They would not be : The cervical discs are between the vertebral bodies. When the vertebral body is injured that may be a compression fracture. The term means that the vertebral body is squashed, much like overloading a thread spool until it splintered.