  Recently, two new constructions of $(v,k,k-1)$ disjoint difference families
in Galois rings were presented by Davis, Huczynska, and Mullen and Momihara.
Both were motivated by a well-known construction of difference families from
cyclotomy in finite fields by Wilson. It is obvious that the difference
families in the Galois ring and the difference families in the finite field are
not equivalent. A related question which is in general harder to answer is
whether the associated designs are isomorphic or not. In our case, this problem
was raised by Davis, Huczynska and Mullen. In this paper we show that the
$2$-$(v,k,k-1)$ designs arising from the difference families in Galois rings
and those arising from the difference families in finite fields are
nonisomorphic by comparing their block intersection numbers.
