Is there a difference between the appoggio technique you advocate and what some writers call belly breathing?
Before addressing the question more directly, some comment about the appoggio is essential. The term is not narrowly related to the management of airflow during singing. It encompasses a complete system of structural support, during which the muscles of exhalation and those of inspiration maintain an antagonistic balance, inciting a stable but dynamic relationship among the intrinsic muscles of the larynx, which in turn are fully supported by the external laryngeal framesupport system. An axial body posture and a relatively low larynx allow the resonator tract above the larynx to function freely. In short, during execution of the appoggio, as part of this physical complex the abdominal-wall musculature not only controls the speed at which the air exits but also and simultaneously induces proper responses directly at the level of the larynx, and in the vocal tract above the larynx.
Belly-breathing advocates probably know that the breath process cannot be controlled by the belly. Perhaps they mean to stress that the abdominal-wall mus-