Digital BW, The Print

Julio Fernanadez wrote, re a perceived misunderstanding of the 
term "D-Max":

<<The dictionary of film and digital Photography defines Dmax as 
follows:
"Dmax: Maximum Density. The most dense area that a medium or image 
capturing device can record."
Matt papers along with matte black ink can record the densest blacks, 
much more so than glossy prints. Which paper has the greater Dmax? 
What I think you meant is that the dynamic range of glossy exceeds 
that of matte. Glossy papers do have a greater dynamic range and are 
capable of greater separation of tones than matte.>>

Glossy paper generally has deeper blacks  - ie greater maximum
optical density or "D-Max" - than matte paper and therefore, as
Julio points out, greater 'dynamic range' (probably better called
'density range' in this case, where density range = D-Max -
D-Min). 
So where is the misunderstanding?

The quoted dictionary definition appears to be inadequate at best, but
that's another issue - or is it the source of the
'misunderstanding'?

Thanks,
Helen