Why say "Hello"?

[L'Impresario]

Yes, in German esp., heil retains the same meaning and from since many hundred years.
But even if looking or sounding the same, a word related to another does not make;)
(hello and kailo~ derived words I mean)

Clearly, at least to me, hæil and salve/ave all have the same Indo-European root. Yet no mention is given in the etymology of hail or hello of the Latin greeting.

The IE root for hæil (and by extension hail) is kailo~, while for hello the dominant theory is that it's a version of the 16th cent. interjection holla (halt, stop) and its father is the Latin illac.