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Yeah, I remember an on-line argument between some individuals about the
'diagonal' descriptive in hexagonal games. One insisted that it was
improper because not only did the target cell have a tenuous connection to
the starting cell but that it involved the shift of three axes on the
field(rather than two) and thus the term 'diagonal' was insufficient.
Another even argued that there were no 'diagonal' moves on the hexagonal
field, merely leaps to orthogonally-connected cells.

There was much venom, and an excessive use of mathematics. In the end,
common use may have won. Few(and there are still some) will now argue about the term 'diagonal' in the description of this form of translation on the hexagonal field.

Perception is probably the greatest factor in game descriptions. How does
a designer relate their concepts to the potential player in such a way that
they can easily visualize them? Building upon common ground is probably a
sound approach. Verbal logic, with minimal use of mathematical
formulae(which some players may have a dis-advantage), is a positive.
Consistency, at least within a given ruleset, is also a necessity.