physical chemistry - Disproportionation of hydrogen peroxide

Hydrogen peroxide is decomposed as follows:

$$\ce{2H2O2 -> 2H2O +O2}$$ This is a disproportionation redox reaction of $\ce{H2O2}$ involving the 2 half reactions $$\ce{H2O2 -> O2 + 2H^+ + 2e-}$$ $$\ce{H2O2 + 2e- + 2H^+ -> 2H2O}$$ But I noticed semantically that it can also be the sum of the two following half reactions: $$\ce{2H2O2 -> 2O2 + 4H^+ + 4e-}$$ $$\ce{O2 + 4H^+ + 4e- -> 2H2O}$$ Both reactions are feasible according to the following:

$$\begin{array}{ccc} \text{Oxidised species} & \text{Reduced species} & E^\circ (\mathrm{V}) \\ \hline \ce{H2O2} & \ce{H2O} & 1.763 \\ \ce{O2} & \ce{H2O} & 1.23 \\ \ce{O2} & \ce{H2O2} & 0.695 \\ \end{array}$$

Can it happen in the second way? If yes, can you explain the mechanism in simple terms?