  There are two versions of Orlicz-Morrey spaces (on $\mathbb{R}^n$), defined
by Nakai in 2004 and by Sawano, Sugano, and Tanaka in 2012. In this paper we
discuss the inclusion properties of these two spaces and compare the results.
Computing the norms of the characteristic functions of balls in $\mathbb{R}^n$
is one of the keys to our results. Similar results for weak Orlicz-Morrey
spaces of both versions are also obtained.
