Since the 8k is pretty much only run as an XC race, I would think that anyone asking your PR would be talking about XC. If you want to give a track split that's fine, but you should at least explain it as such.
They do, but they have different connotations, and that's the whole point of your thread. If you set your 5000m PB as a split in a 10000m race, you could certainly claim that as your best 5000m time, and finding out that it was a split only serves to tell us that you could have gone even faster. But 8k races are coded as cross country, and usually it's easier to run a given pace for 10000m on the track than it is to run that pace for 8k cross country. So it could be seen as misleading to quote a track time of any sort, even a split as your 8k PB, similar to how running an aided Boston marathon is slightly illegitimate as a marathon PB, even though in context it's a legitimate race.
[And all of this is without getting into short cross country courses]
I would just say "around 25 minutes" or "around 25-flat". If pressed "I ran 25:20 for 8k cross country, but 24:46 as part of a 10k on the track". If the context is track (or road) racing, you're certainly justified to say 24:46 without further explanation.