a person in the industry will have a good idea of the definitions (as we can see they vary!)
No "they" don't vary, what varies is the degree of misunderstanding, misinterpretation, and so forth.
I have lived through (quite literally) the whole development of performance standards certification from SFAR 422B on, and it is a pity that efforts over the years to eliminate flawed understandings has been obviously so unsuccessful.
Part of the history: In the '70s and early '80s, there were a series of rejected takeoff accidents, some with seriously fatal consequences to passengers, crew, and in several very sad cases, people on the ground.
Among other things, this resulted in a major study by the ATA, which also included a number of non-US airlines, of which Qantas was one.
The study was to find out what pilots really knew about aircraft performance, what they had learned, where and how they had learned, been examined etc.
A core finding was a fundamental misunderstanding of V1, its derivation, and what it means in the flight deck.
As we see here, in this thread, there is wide deviance from the actual definitions. Some of you have talked about manufacturer information, used to derive manual information. What you really mean is somebody employed by a manufacturer, with an imperfect knowledge of the subject, has passed along, in good faith, a flawed explanation, which has been "interpreted" by the airline person, and something has wound up on a manual, and treated as gospel by probably generations of crews. But it was wrong.
There were several good examples of that in Qantas manuals back in the 60s, it was only when a pilot who had professional qualifications and experience in aircraft certification, arrived on the scene, the errors were corrected.
Specifically, in one case, the "Qantas" explanation of "geometry limited" on takeoff was completely wrong. There were other, they all had one thing in common, the information was not derived from source, but were misconceptions built on misunderstandings by pilots whose executive positions did not qualify them as performance engineers.
In the early days of the B707-338C in Qantas, the instructions for trimming were quite wrong. That one I remember very very well.
And, up to and including the B767 program, sometimes even the performance engineers get it wrong.
At about the same time, in parallel, but not directly related, an AFAP tec. team was looking at the whole issue, including military approaches, because at the time there was much interest in performance monitoring and "wet runway" operations ---- is the aircraft really accelerating "by the book", but that is a whole other subject.
Back to V1, the disturbing outcomes of the flawed knowledge clearly illustrated why a mindset on the flightdeck contributed to disastrous rejected takeoffs.
A major retraining program, originally designed by Delta, was taken up by all members of ATA, and most members of IATA, and was carried out through briefings and changes to simulator renewal or cyclic training programs, and I well remember the Qantas program, and the resistance of quite a few pilots (and not necessarily the older pilots) to having their fondly held misconceptions about V1 disturbed.
Bottom line: The certification definition is as I have said, the meaning on the flight deck is as I have said, and a proper first principles understanding of that part of certification allows no other definition.
Tootle pip!!
PS 1: A Boeing have always been happy to admit, their aeroplanes go better than they stop.
PS 2: Most pilots are most paranoid about runway length, and accelerate/stop distances, but the record show that a very significant number of rejected takeoffs result in loss of directional control, and leaving the side of the runway.
PS 3: There were some quite fundamental errors in the RR book "The Jet Engine", I don't know if they have been corrected in later editions. D.P Davies, in "Handling the Big Jets", even misinterprets his own ARB certification requirements, and largely ignores (except where he criticizes) the US certification of the B707. In my opinion (having flown both extensively) the ARB modifications to a B707 for a British C.of A were dangerous.