How does Ammonia and water mixture works in an absorption refrigeration? As per one of the questions in this site $$\ce{NH3 + H2O -&gt; NH4 + OH}$$

However, per another perspective in absorption refrigeration


  The mixture is placed in the same container. Then when it is heated the mixture is separated and $\ce{NH3}$ changes phase, becomes a gas which moves further to cooling, while water is trapped down in the reservoir.


Which one is correct?
The difference between the absorption refrigerator and the more common refrigerator is that there is no compressor in the absorption refrigerator.  The Absorption refrigerator still needs a way to convert the evaporated refrigerant back to a liquid state.  Instead of compressing it in one step, the evaporated refrigerant is absorbed by a liquid.  The liquid is heated and the refrigerant evaporates from the liquid.  The refrigerant is cooled in a heat exchanger and condensed.  It is now a liquid and ready to go back through the cycle.

The equation you have written is a reaction between ammonia and water.  This reaction will occur in an absorption refrigerator that uses water as the absorber and ammonia as the refrigerant.  The equilibrium constant of the reaction is low so it is not accounted for in a discussion of how an absorption refrigerator works.