Flungdung,
Whilst I do agree with you re the definitions, consider the following...
The scenario...
On an IFR departure with cloudbase between 50 and 100ft, vis 150 -200 metres and the nearest single engine diversion almost an hour away (all legal for North Sea Cat A ops).
The problem...
Just after TDP, but before going into cloud, with the runway ahead of you still visible, you have an engine fire warning, would you continue the take-off, or put it back on the ground?
I'm sure I know what I would do. If I could get it back on the ground that's where it would go regardless of any 'legal definitions'.
Brom.