Current quarks (also called naked quarks or bare quarks) are a description of valence quarks as the cores of the quark particles that are the invariable parts of a hadron: their non-virtual ("real" or permanent) quarks with their surrounding "covering" of evanescent gluons and virtual quarks imagined stripped away. In quantum chromodynamics, the mass of the current quarks is called the current quark mass, as opposed to the much larger mass of the composite particle which is carried in the gluon and virtual-quark covering. The heavier quarks are large enough for their substantial masses to predominate over the combined mass of their virtual-particle "dressing" or covering, but the lighter quarks' masses are overwhelmed by their evanescent covering's mass-energy; the light quarks' core masses are such a small fraction of the covering that the actual mass values are difficult to infer with any accuracy (hence, the data listed below for the light quarks are fraught with caveats).
The constituent quark, in contrast, is a combination of both the "naked" current quark and its "dressing" of evanescent gluons and virtual quarks. For the lighter quarks, the mass of each constituent quark is approximately 1 /3 of the average mass of the proton and neutron, with a little extra mass fudged in for the strange quark.