Yes, there is a significant difference: although the quasiparticle shows the same behavior as the 'real' particle in some respects, it shows different behavior in other respects.
For instance, the quasiparticle can be destroyed by the addition of some heat to the system, while a 'bare' Majorana fermion would not cease to exist in the presence of that amount of energy.
Analogy: in certain measurements (e.g. distribution of reflected light frequencies), a red circle is indistinguishable from a red sphere. However, in other respects (e.g. distribution of reflected light intensity), they are quite different.
For instance, the quasiparticle can be destroyed by the addition of some heat to the system, while a 'bare' Majorana fermion would not cease to exist in the presence of that amount of energy.
Analogy: in certain measurements (e.g. distribution of reflected light frequencies), a red circle is indistinguishable from a red sphere. However, in other respects (e.g. distribution of reflected light intensity), they are quite different.