Switching equivalence of strongly regular polar graphs

We prove the switching equivalence of the strongly regular polar graphs $N{O}^{\pm }(4m,2)$, $N{O}^{\mp }(2m+1,4)$, and $\mathrm{\Gamma }(O^{\mp }(4m,2))$ plus an isolated vertex by giving an analytic description for them and their associated two-graphs.