Anyone from Airbus' marketing area is probably grimacing, and from Boeing's is probably grinning: BBJ stands for Boeing Business Jet, I believe (although maybe it will turn into the standard - like the Poms call vacuum cleaners "Hoovers"), but is actually a modified 737-700 (with a modified -800 wing, I believe).
The PrivatAir/Lufthansa (for it is indeed a one-and-the-same joint effort) is an ACJ, short for Airbus Corporate Jet, modelled on the A319.
(careful doing range calculations based on the A319 data, as they may have different fuel capacities)