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Another way to view the difference between a DLL and a PLL is that a DLL uses a variable phase (=delay) block where a PLL uses a variable frequency block.
In the Control Systems jargon, the DLL is a loop one step lower in order and in type with respect to the PLL, because it lacks the 1/s factor in the controlled block: the delay line has a transfer function phase-out/phase-in that is just a constant, the VCO transfer function is instead GVCO/s. In the comparison made in the previous sentences (that correspond to the figure where the integrator, and not the flat gain, is used), the DLL is a loop of 1st order and type 1 and the PLL of 2nd order and type 2. Without the integration of the error signal, the DLL would be 0th order and type 0 and the PLL 1st order and type 1.