Strictly speaking, Vaughn's variant spell was not an improvement on Sectumsempra, but simply another way of using it.
He had disregarded Sectumsempra's ability to leave wounds that would not heal, strengthening its cutting effect instead and turning the spell into a pure "blade."
Of course, if Sectumsempra were that simple, Snape would hardly qualify as a genius.
Sectumsempra's greatest strengths lay in the surprise of its invisible cuts and its nature as a "nonphysical attack."
At its core, Sectumsempra did not create a blade to attack its target. It acted directly on the target, producing an effect that resembled a cut from a sharp blade.
There was a fundamental difference between magic and a purely physical attack.
But Sectumsempra had not reached the absurd level of creating wounds out of thin air. The spell still needed a "medium" to take effect.
Blood was Sectumsempra's medium!
That was why Sectumsempra could not affect inanimate objects or harm Inferi.
Vaughn's variant of Sectumsempra strengthened this effect. In a sense, the two North American wizards who had died from it could be said to have had their bodies and necks sliced open by their own blood.
After killing the third North American wizard, Vaughn waved his wand again, preparing to Apparate and swiftly finish off the remaining three. But the spell failed. He remained standing behind the North American wizard's headless corpse.
An Anti-Apparition Jinx!
Vaughn's pupils contracted slightly. Before, he had only suspected that DeSantis was here, secretly helping the North American wizards. Now he was certain.
There had been no Anti-Apparition Jinx here when he arrived, and less than a minute had passed between his entry into the villa and his killing of the third North American wizard.
Vaughn could not imagine anyone other than a legendary wizard casting an Anti-Apparition