I think mps is the inner structure of DMRG. And also mps is the reason why DMRG can succeed for its catching low entanglement of 1D systems. While considering systems in PBC conditon, VMPS can acheive much better results than DMRG. In some way, I think DMRG is nothing more than a special version of VMPS approach. DMRG's theory lies in mps.