The interaction is called 'charged' because the W bosons coupling to the charged currents must have electric charge. The charged current that gives the interaction its name is that of the interacting particles, in a charged combination. For example, the charged-current contribution to the
elastic scattering amplitude
where the charged currents describing the flow of one fermion into the other are given by
Charged current interaction is the most easily detected of the interactions of the weak force. The weak force is best known for mediating nuclear decay. It has very short range, but is the only force (apart from gravity) to interact with neutrinos. The weak force is communicated via the W and Z exchange particles. Of these, the W-boson has either a positive or negative electric charge, and mediates neutrino absorption and emission by or with an electrically charged particle. During these processes, the W-boson induces electron or positron emission or absorption, or changing the flavour of a quark as well as its electrical charge.
By contrast, the Z particle is electrically neutral, and exchange of a Z-boson leaves the interacting particles' quantum numbers unaffected, except for a transfer of momentum, spin, and energy.
Because exchange of W bosons involves a transfer of electric charge (as well as a transfer of weak interaction charge), it is known as "charged current". By contrast, exchanges of Z bosons involve no transfer of electrical charge, so it is referred to as a "neutral current". In the latter case, the word "current" has nothing to do with electricity – it simply refers to the Z bosons' movement between other particles.