Is a `Majorana mass' fermion just the same as a genuine (really neutral) Majorana particle?

The idea of a `Majorana mass' to make a chiral neutrino really neutral is here reconsidered. It is pointed out that such an approach, unlike Majorana's (non-chiral) old one, does not strictly lead, in general, to a true self-conjugate particle. This can be seen on directly using the basic definition (or fundamental representation) of charge conjugation $C$ in Quantum Field Theory, as an operation just acting on annihilation and creation operators and just expressing particle--antiparticle interchange. It is found, indeed, that the `active' and `sterile' whole fields which can be obtained from mixing the chiral components of two mutually charge-conjugate Dirac fields are themselves `charge conjugate' to each other (rather than individually self-conjugate). These fields, taken as mass eigenfields (as in the `Majorana mass' case), are shown to describe particles carrying pseudoscalar-type charges and being neutral relative to scalar-type charges only. For them, `$CP$ symmetry' would be nothing but pure mirror symmetry, and $C$ violation (already implied in their respective `active' and `sterile' behaviors) should then involve time-reversal violation as well. The new (no longer strictly chargeless) `Majorana mass' neutrino model still proves, however, neither to affect the usual expectation for a neutrinoless double $\beta$-decay, nor to prevent `active' and `sterile' neutrino varieties from generally taking different mass values. One has, on the other hand, that any fermion being just a genuine (i.e. really self-conjugate) Majorana particle cannot truly exist in two distinct $-$ `active' and `sterile' $-$ versions, and it can further bear only a unified mass kind which may at once be said to be either a `Majorana-like' or a `Dirac-like' mass kind.