By definition, current flows from cathode to anode in any type of electrical loop, including both galvanic and electrolytic cells (electrical flow is the opposite, because oxidation occurs at the anode and reduction occurs at the cathode).
The tricky thing is that the anode in a galvanic cell is turned into the cathode in the electrolytic cell, because the applied voltage is forcing the reaction to run backwards. So while the current reverses direction, it is still cathode to anode, because the electrodes have also been reversed.
I think you are using BR books, so if you can look at Figures 10-5 and 10-7, you'll see that both electrodes contain the exact same solid and solute in both cells, but because voltage is being applied in 10-7, the electrons flow in the opposite direction of 10-5 and the anodes and cathodes are reversed.