  We discuss and compare two different types of confinement in bilayer graphene
by top and bottom gating with symmetrical microelectrodes. Trivial confinement
corresponds to the same polarity of all top gates, which is opposed to that of
all bottom ones. Topological confinement requires the polarity of part of the
top-bottom pairs of gates to be reversed. We show that the main qualitative
difference between trivial and topological bound states manifests itself in the
magnetic field dependence. We illustrate our finding with an explicit
calculation of the energy spectrum for quantum dots and rings. Trivial
confinement shows bunching of levels into degenerate Landau bands, with a
non-centered gap, while topological confinement shows no field-induced gap and
a sequence of state branches always crossing zero-energy.
