  We compare three different approaches to describe a magnetic island in a
generic toroidal plasma: (i) perturbative, from the perspective of the
equilibrium magnetic field and the related action in a variational principle
formulation, (ii) again perturbative, based on the integrability of a system
with a single resonant mode and the application of a canonical transformation
onto a new island equilibrium system, and (iii) non-perturbative, making use of
a full geometric description of the island considered as a stand-alone plasma
domain. For the three approaches, we characterize some observables and discuss
the respective limits.
