I don't know--I understand the basics of overtones, but I'd never heard of covered and uncovered singing before.    As I understand it, harmonics are created by multiple voices sounding different tones, while overtones are created around the single voice, but I suppose overtones are a kind of harmonic on the single voice.

A quick check on wikipedia tells me I've got it wrong:

Overtone - Wikipedia, the free encyclopedia

An overtone is a natural resonance or vibration frequency of a system. Systems described by overtones are often sound systems, for example, blown pipes or plucked strings. Approximate harmonic overtones on a string

If such a system is excited, a number of sound frequencies may be produced. These frequencies, are usually, but not always, a close approximation to an integer multiple of a lowest resonance frequency. Thus, overtones and harmonics should not be confused or interchanged. By definition a harmonic is an exact integer multiple of a fundamental frequency, whereas in most systems, overtones are never exact integer multiples of a root frequency. For example, the first overtone of a circular drum is approximately 2.4 times its fundamental resonance frequency.

Don't fight forces, use them R. Buckminster Fuller.