Which of these is best described as an acid-base reaction?

KCl + NH4NO3 = KNO3 + NH4Cl

NH3 + H2O = NH4 + OH

Where are electrons transfered? Not in the first one.

In the second, you are missing something critical..

NH3 + H2O >> NH4+1 + (OH)-1

now, notice charge flowed between the reactants. On gave up a hydrogen to the ammonia, and lost its electron (that is why it has a +1 charge now).