Corporate Flight departments tend to be run in different ways in the UK and in the USA. In Britain, they are often under the control of the Chief Pilot, in conjunction with the Chairman's office, and just used by the directors, sometimes commonly just one of them, so they are typically small. In the US they are integrated with the company travel organiser for everyone, as business trips by air are much more common, and you maybe don't know at travel request time whether you will suddenly be put onto the company aircraft with various others who happen to be going the same way. One I talked with said it was no great shakes, you could be sent out by exec jet but back by airline to a different terminal or even airport, which was a nuisance for parking your car, while the flight catering was minimal or even nothing at all.
I believe the longstanding Ford operation out of Stansted was very much on the US pattern, seating pitch like an airliner in economy, and often taking urgent production line parts in the hold. Those with reservations could be suddenly bumped by someone more senior in the company. I'm sure we will have some on here who used to fly for them.
Not a tale from a flight department, but the major company I was with long ago had the branch manager in Newcastle who was ex-RAF aircrew, and to help keep his hours current when there was a mainstream meeting in London he would pool the train fare expenses of all the salesmen going, and hire a light twin for them all from Newcastle down to Leavesden or somewhere. His immediate boss the sales director did not like flying, but went along with it to keep face. Manager, of course, used to put him in the co-pilots seat at the front, and make various asides as they were going along, on the lines of not being quite certain where they were, or the fuel gauge lower than expected ...
