  We reconsider the topological interpretation of magnetic helicity for
magnetic fields in open domains, and relate this to the relative helicity.
Specifically, our domains stretch between two parallel planes, and each of
these ends may be magnetically open. It is demonstrated that, while the
magnetic helicity is gauge-dependent, its value in any gauge may be physically
interpreted as the average winding number among all pairs of field lines with
respect to some orthonormal frame field. In fact, the choice of gauge is
equivalent to the choice of reference field in the relative helicity, meaning
that the magnetic helicity is no less physically meaningful. We prove that a
particular gauge always measures the winding with respect to a fixed frame, and
propose that this is normally the best choice. For periodic fields, this choice
is equivalent to measuring relative helicity with respect to a potential
reference field. But for aperiodic fields, we show that the potential field can
be twisted. We prove by construction that there always exists a possible
untwisted reference field.
