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 ##23.4^o## and vertex at Earth's center. The nutation compounds with this to produce a gentle nodding..

Both precession and nutation are due to gravity of nearer Earth and farther Sun on 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 inhttp://space-geodesy.nasa.gov/multimedia/EarthOrientationAnimatioEOAnimation.html ..