On two-intersection sets with respect to hyperplanes in projective spaces

In \cite{BLLA} a construction of a class of two-intersection sets with respect to hyperplanes in $PG(r-1,q^t)$, $rt$ even, is given, with the same parameters as the union of $(q^{t/2}-1)/(q-1)$ disjoint Baer subgeometries if $t$ is even and the union of $(q^t-1)/(q-1)$ elements of an $(r/2-1)$-spread in $PG(r-1,q^t)$ if $t$ is odd. In this paper we prove that although they have the same parameters, they are different. This was previously proved in \cite{BABLLA} in the special case where $r=3$ and $t=4$.