An electron is assumed to be a point particle that does not have structure. Why does it have left-handed and right-handed components? Does this imply that the electron has structure or volume?
Whether you are asking if there is an intuitive way to understand the difference between left and right handed electrons, no, the difference is not classical, it depends on the QM theory.
All the difference that matters comes from QM theory, but in the classical case EM is P symmetric. In this classical case you cannot distinguish between left and right handed electrons, like in classical EM.
Now if the theory (QM) brakes P symmetry, you can differentiate, since one particle will interact differently then the other one. The best way is in weak interactions, which violate P symmetry, and so only left handed electrons and neutrinos will (or right handed antiparticles) create a weak isospin doublet.
Devices used to measure electron helicity is, which would be polarization, are Moller and Compton polarimeter.
These helicity measurements, scatter electrons off another polarized particle (which we know upfront) so the electron's polarization will be known too.