It is almost silly to compare when dealing with singers at this level. However, it is small differences like those that show up down the line and shorten careers. We can hear a definite comfort difference between the two Corelli clips and a very discernible discomfort in Giacomini's performance. The lowered back of the tongue alters the natural resonance of the vocal tract causing Giacomini considerable insecurity in parts of the aria and Corelli a milder discomfort in his first clip. The ease of production in Corelli's studio recording is vastly different from the live performance.
If we were to compare Corelli's second recording, which is resonance-wise pretty pure, with say Di Stefano who we know sang a thinner production with a high larynx, we can then understand the idea of "gola aperta" or open throat.
It is a relative thing. It is possible to take the open throat too far as I did in my recording of "Di Provenza" but it might still be called "aperta". However it loses closure and therefore lacks presence. In the case of the depressed larynx as in the Giacomini clip and to a much smaller extent the first Corelli clip, we would have to assign the term "voce ingolata" or "swallowed voice." In the case of Di Stefano, his approach is called "voce spalancata" or "wide open"!