  Building on results from the Magnetism in Massive Stars (MiMeS) project, this
paper shows how a two-parameter classification of massive-star magnetospheres
in terms of the magnetic wind confinement (which sets the Alfv\'en radius RA)
and stellar rotation (which sets the Kepler co-rotation radius RK) provides a
useful organisation of both observational signatures and theoretical
predictions. We compile the first comprehensive study of inferred and observed
values for relevant stellar and magnetic parameters of 64 confirmed magnetic OB
stars with Teff > 16 kK. Using these parameters, we locate the stars in the
magnetic confinement-rotation diagram, a log-log plot of RK vs. RA. This
diagram can be subdivided into regimes of centrifugal magnetospheres (CM), with
RA > RK, vs. dynamical magnetospheres (DM), with RK > RA. We show how key
observational diagnostics, like the presence and characteristics of Halpha
emission, depend on a star's position within the diagram, as well as other
parameters, especially the expected wind mass-loss rates. In particular, we
identify two distinct populations of magnetic stars with Halpha emission:
namely, slowly rotating O-type stars with narrow emission consistent with a DM,
and more rapidly rotating B-type stars with broader emission associated with a
CM. For O-type stars, the high mass-loss rates are sufficient to accumulate
enough material for line emission even within the relatively short free-fall
timescale associated with a DM: this high mass-loss rate also leads to a rapid
magnetic spindown of the stellar rotation. For the B-type stars, the longer
confinement of a CM is required to accumulate sufficient emitting material from
their relatively weak winds, which also lead to much longer spindown
timescales. [abbreviated]
