I have never been able to get my head around
Is it a "Private" flight
Is it a "Charter" flight
Ah yes, "Private Jet" is a term synonymous with VLJ's and upwards.
So you are chartering a "Private Jet" style of aircraft.
WiKi says:
"A business jet, private jet, or bizjet is a jet aircraft designed for transporting small groups of people, typically business executives and high-ranking associates."
Good point, it's all in the engrish.