Harmonic Chant is another popular name for Overtone Singing. By using the word ‘Chant’ it appeals to a slightly different audience associating it to Gregorian Chant and giving it a more spiritual context. However, this is mostly just marketing. Personally I see Overtone Singing as the generic overarching term for all such vocalisations that seperate the Fundamental from the Overtones audibly. Harmonic Chant is a subset preferred by certain artists such as David Hykes.

There is a technical difference as well which is that all harmonics are Overtones but not all overtones are harmonics. Harmonics are by definition  perfect whole number ratios of the fundamental frequency. Overtones can be distorted by physical anomalies such as tightness and thickness of a string.

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