Meaning of "unification of interactions"

Unification loosely means subsumption into the same theoretical framework. Electricity and Magnetism, quite different from each other under normal circumstances, were unified by Maxwell through his equations that related them as different aspects/pieces of the same theory, and they need each other for the theory's consistency. The electromagnetic and weak interactions are unified, to the extent they are both neatly interlocked pieces of the same ??(2)×?(1) gauge theory, and their characteristic couplings are related, so the electromagnetic coupling $e=gg'/sqrt{g^2+g'^2}$, where g is the weak charged current coupling, and g' is the weak hypercharge coupling related to the weak neutral current. This unified theory is controlled by a characteristic energy scale $vapprox 0.25 TeV$.

Scattering an electron off a nucleus through the mediation of a photon (QED) carrying "small" (compared to your v) energy looks very different from a low-energy β-decay of a neutron to a proton, electron and antineutrino, mediated by a heavy (80GeV) W boson, which carries off a very small energy, the energy of the lepton pair, not to mention the peculiar chiral structure of this event. The weak decay is very short-range, and the heaviness of the virtual W weakens the strength, and hence probability, of the interaction enormously. So, at small energy transfers, the weak interaction is much, much weaker than the EM one.