I don't know if this gets at an eternal question better but:
The modern "Biarritz the Hole" most often seen, created or preserved, is a one shot hole of usually 190-230 yards, with a unusually long rectangular green, containing a perpendicular gully near its middle which bisects the green into two distinct shelfs. There are most often guardian bunkers left and right paralleling the sides of the green. Less often seen, but historically significant, are some older Biarritzes which make the long shot carry water most of the way...
because these are older and closer to the original importation of the design, there is a great deal of question as to whether the Biarritz was...
...an amalgam copy of two holes on the Dunn's course, one being another shorter hole that carried an ocean inlet called "The Chasm?"
...whether it's the graft of another singular hole on the French course, also played over similar terrain as "The Chasm" hole?
...whether the first version of this template wasn't an Approach concept from Scottish models (like Machranish or St. Andrews 18th Valley of Sin) married to the thrills of the shorter Chasm hole.
No matter what your conclusion about the provenance and evolution of Biarritz the Hole...Biarritz the Landform is probably the more salient GCA point in your inquiry.
When looking at the Landform model and not the hole model, then a Biarritz may be defined thus:
"A short raised green pad segregated from its immediate, open approach by an abrupt contour resembling a gully."
In 100 years of evolution as the style was promulgated, the "immediate, open approach" and the "contour resembling a gully" were maintained as actual green surface, not just firm fairway grass, thus resulting in both intended and evolved Biarritzes where the thing mowed as and called the Green is the entire landform.
The older style "Not Green in Front" is often disputed to be the original style and those with green surface the entire way somethign of a bastardization; it is a point capable of question.
But the Biarritz idea... before it's got any water, whether or not it's a par 3... whether or not the entire approach and target are is kept as green surface...is that the topography of approach has a collecting trap door that must be navigated for ultimate success.
That is the reason just about every comment you will hear fro m the board says..."Pin must be in rear shelf...that shelf is the defended target."
cheers
vk