  We consider two types of magnetic Josephson junctions~(JJ). They are formed
by two singlet superconductors~S and magnetic layers between them so that the
JJ is a heterostructure of the S$_{\text{m}}$/n/S$_{\text{m}}$ type,
where~S$_{\text{m}}$ includes two magnetic layers with non-collinear
magnetization vectors. One layer is represented by a weak ferromagnet and
another one---the spin filter---is either conducting strong ferromagnet
(nematic or N\nobreakdash-type JJ) or magnetic tunnel barrier with
spin-dependent transparency (magnetic or M\nobreakdash-type JJ). Due to spin
filtering only fully polarized triplet component penetrates the normal n~wire
and provides the Josephson coupling between the superconductors~S. Although
both filters let to pass triplet Cooper pairs with total spin~$\mathbf{S}$
parallel to the filter axes, the behavior of nematic and magnetic JJs is
completely different. Whereas in the nematic case the charge and spin
currents,~$I_{\text{Q}}$ and~$I_{\text{sp}}$, do not depend on mutual
orientation of the filter axes, both currents vanish in magnetic~JJ in case of
antiparallel filter axes, and change sign under reversing the filter direction.
The obtained expressions for~$I_{\text{Q}}$ and~$I_{\text{sp}}$ show clearly a
duality between the superconducting phase~$\varphi$ and the angle~$\alpha$
between the exchange fields in the weak magnetic layers.
