What is the difference between precession and nutation in terms of the earth's rotation?
Precession motion of polar axis is over a double right cone, with semi-vertical angle
Both precession and nutation are due to gravity of nearer Earth and farther Sun on the Earth that varies with changing distances. The inclination 5 deg of the orbital plane of Moon to the Earth[s orbital plane (ecliptic) and the inclination of the equatorial bulge of the Earth at 23.4 deg to the ecliptic are also contributors. .
The period of the long-term precession motion is about 260 centuries. In this motion, the poles trace a small circle of radius nearly 2530 km, about the normal to the ecliptic
The short-term nutation (nodding) of the polar axis is having a compounded period of about 18.6 years from oscillations with smaller periods, up to as low as some days. This 18.6 y is in sync with the the period for the motion of lunar nodes on the ecliptic.
This is my verbal explanation, with some data. You have a good graphical depiction in