You described already the differences, in redox reactions the electrons are transferred, what means the oxidation number of atoms will change, like Fe2+ => Fe3+ + e- or 2 H+ + 2 e- => H2
In acid base reaction the protons (hydronium) are transferred. At least you get neutralisation like H+ + OH- => H2O or NH4+ + NH2- => 2 NH3, etc.