Cross-fire, Flanking Fire

[cjsiam]

In PG it is cross-fire
In IA it is flank fire.

Is there a difference in tracing through a "hex" and a non-adjacent "hexside"?

If you fire from one hex into a adjacent hex, which one did you go through? By most definitions, neither. You fire out of one and into the other.

And in any case of firing into a hex, you cross a hexside boundary....only one, and always.

The stricture "Through a non-adjacent hex" --- is it topologically equivalent to "Through a non-adjacent hexside" ?
I interpret it to be so---are there any counter examples?
Would that not alleviate any question?...only caveat (in either case) is an "along the hex spine" shot -- it is placed in the least advantageous hex for the firer....and it works?
?