Can a hinge joint technically allow rotatory motion?

Let’s use a hinge joint and pivot joint as examples.

When talking about the difference between them in terms of movements permitted, I see that on any websites and textbooks, the term ‘rotation’ is applied to pivot joint only rather than hinge joint.

For example, according to Moore Clinically Oriented Anatomy 10th edition.

Hinge joints permit flexion and extension only, movements that occur in one plane
(sagittal) around a single axis that runs transversely; thus, hinge
joints are uniaxial joints.

Pivot joints permit rotation around a central axis; thus, they are
uniaxial. In these joints, a rounded process of bone rotates within a
sleeve or ring.

I never see the word ‘rotation’ being used to describe hinge joints’ motion, however, doesn’t hinge joint technically allow rotation, just that the rotation for hinge and for pivot joints are over a different axis? For example, at the anatomical position, flexion in the elbow’s hinge joint involves rotating the joint along the tranverse axis.

So my question is, can a hinge joint technically allow rotatory motion? If not, am I misunderstanding what is meant by ‘rotation’/’rotatory motion’?