  In 2011, Penttila and Williford constructed an infinite new family of
primitive $Q$-polynomial 3-class association schemes, not arising from distance
regular graphs, by exploring the geometry of the lines of the unitary polar
space $H(3,q^2)$, $q$ even, with respect to a symplectic polar space $W(3,q)$
embedded in it.
  In a private communication to Penttila and Williford, H.~Tanaka pointed out
that these schemes have the same parameters as the 3-class schemes found by
Hollmann and Xiang in 2006 by considering the action of $\mathrm{PGL}(2,q^2)$,
$q$ even, on a non-degenerate conic of $\mathrm{PG}(2,q^2)$ extended in
$\mathrm{PG}(2,q^4)$. Therefore, the question arises whether the above
association schemes are isomorphic. In this paper we provide the positive
answer. As by product, we get an isomorphism of strongly regular graphs.
