Explain how a redox reaction involves electrons in the same way that acid-base reaction involve protons

Redox reaction stands for reduction/oxidation reaction whereas acid-base reaction involves acid and base in its reaction. 
Acid-base reaction involves the transfer of protons whereas redox reaction involves the transfer of electrons. Thus in both the case, a charged species is transferred from one molecule to another. 
In case of redox reaction, oxidation involves loss of electrons and reduction involves gain of electrons. Thus, one substance gets oxidized (acts as reducing agent and donates electrons) while other gets reduced (acts as oxidizing agent and gains electrons).
Similarly, in acid-base reaction one substance accepts proton while other releases proton. Thus, one substance is called conjugate acid (the base that accepts protons) and other is called conjugate base (acid that donates protons). 
Thus reducer and oxidizer are analogous terms for acid and base respectively.