uh? You have the order of the equations around the wrong way.
At anode, H2O + e --> 1/2H2 + OH
At cathode, H2O --> 1/2O2 + 2H + 2e. (this equation was lower down - the 1.23V one)
Re: second part, yeah. Electrolytic require energy input, galvanic are spontaneous and produce energy.