In connection with topological quantum computing I encountered term Majorana fermions. According to Wikipedia these are:
A Majorana fermion, also referred to as a Majorana particle, is a fermion that is its own antiparticle.
The Wiki also states
With the exception of the neutrino, all of the Standard Model fermions are known to behave as Dirac fermions at low energy (after electroweak symmetry breaking), and none are Majorana fermions. The nature of the neutrinos is not settled - they may be either Dirac or Majorana fermions.
I am a little bit confused by this. Since neutrinos are electrically neutral, I would expected that they are their own antiparticles. At the same time, I know that there is also a lepton number which is negative for antiparticles. So neutrino and anti-neutrion can still differ in value of the lepton number.
Does this all mean that Majorana fermions and anti-fermions have positive lepton number?
In connection to quantum topological computing where so-called anyons quasiparticles are used, the Wiki states
In superconducting materials, a Majorana fermion can emerge as a (non-fundamental) quasiparticle, more commonly referred to as a Bogoliubov quasiparticle in condensed matter physics. This becomes possible because a quasiparticle in a superconductor is its own antiparticle.
So, why in case of quasiparticles, they are their own antiparticles and in case of neutrinos they are not?
I would appreaciate a more or less laymen explanation, if possible, as I am not well trained in mathematical background of particle physiscs.