It is all based on some fairly sketchy assumptions about cooling airflow, and two different sets of tests done by different teams at different times. 

Horizontally, most of the influence on a cable comes from its closest immediate neighbours, and progressively less from those further away, By the time you get to something like 5 or 6 cables wide the ones in the middle may as well be part of an infinite array of cables. If you look at the tables you see that the effect of one more cable when you go up gets quite small. The greater the spacing, the less  the cooling air coming up the gaps is  heated or slowed down by the adjacent cables. It is not really true to say ' no effect' at any distance, even out to very far indeed, so more a case of just how far out do we no longer care, ignoring de-rating of  5%, 2 %, 1% ? it is a bit of a judgement call, and different authorities have rolled that dice a bit differently over the years.

To further muck it up, the assumption that a cable diameter spacing has the same de-rating factor for both thick and thin cables is  a bit off, in practice the way chimney convection currents start to form eddies in larger gaps, means that rule of thumb  tends to over-cook thin cables and thin gaps while fat cables with larger gaps run a bit cooler than expected. The saving grace is that very rarely are all cables at full load at the same time. Indeed quite often we know the total supply to the building or the dis-board or whatever, and can know an upper bound of how many can be fully loaded at once.

Not perhaps your original question but note that this does not work at all when cables are stacked vertically, as the heat from all the cables below rises and pre-heats the ones above.

Neither table is truly 'correct' of course, just good enough guidance to avoid a serious problem.

Mike.