I think that we may add that in the confining phase, the QCD-string descritpion of quarks (say, mesons, which are bound states of quark/anti quarks) is that these particles sit at endpoints of "QCD-strings" (I use "" to distinguish this from the normal superstring which is a well defined object, though it failed for the moment at describing exactly confinement in non-supersymmetric theories). This QCD-string is then a sort of "flux-tube" for the strong interaction, and in this picture, it is a more fundamental object than the quarks which sit at the endpoints, and it rather describes "partons" (i.e. it includes gluons in addition to quarks and mix them up in a string).
Of course this is not a well understood formulation, were it be the case confinement would have been solved.
Very insightfull steps in this direction are obtained for supersymmetric QCD like theories for which you take the number of colors N to infinity and the coupling constant of your theory to zero (the so called 't Hooft limit).