I get what you mean BB.
It depends on who is benefitting. When we're talking about certificates and such "Well, its our Embraer division. Its a part of mainline US Airways..." or training "we can train them in days! These are employees with years of experience, silly FAA..." or unemployment "We offered them a US Airways job, no welfare for them, even if it is more money!"
But to the employees... "You will be eligible for medical benefits in six months. You are a new hire at MidAtlantic Airways and you should be happy to be welcomed to this new airline and to have an airline job, you lazy, overpaid pig." "You should sign a contract to work here for a year so you don't run back off to mainline." "We dont care that you've got five years with the company, American Eagle flight attendants with two weeks of seniority fly 30 seat props for that pay, so you will fly a 75 seat jet for that pay, at this new airline."
I see what you mean... its spun differently to suit the company's needs. If it were a true division of mainline, it would have US Airways on the side and we'd be calling it the Small Jet Division or Short Haul Division or something. Instead it says US Airways Express- Operated by MidAtlantic Airways on the plane.
MetroJet was a division, at least for the pilots. Shuttle was a W/O/division at one point. International is a division crew-wise. Mid is a a wholly-owned airline on the mainline certificate.