My understanding as far as the UK is concerned (I don't have a reference but it's based on practice, over forty years, at more than twenty different organisations and almost as many maintenance facilities):
Commencing taxy with the intention of flying, the flight time starts when you start to move and finishes when you stop to subsequently shut down. This is time for your personal log book (almost universally rounded to the nearest 5 minutes or a decimal equivalent. (Taxying to or from a fuel station or to load or unload is not logged anywhere except perhaps the airfields own log of movements) If, for any reason, the flight is abandoned before entering the runway no time is logged. If a take off is rejected that should be entered as such in the personal log book.
Only airborne time should be entered in airframe or engine log books.