No, they aren't. This is just sloppy wording in the article. The concept of sets is deeply established in mathematics and when you talk about multisets rather than sets you have to state this explicitly.

That's what I thought -- it was what I was taught in school. But I was also taught that no one can agree on terminology.

In this, case, it's trivial to word the problem a "sets of objects, each with integer size, partition into sets of equal sum size". It is still polite to state that explicitly outside of the sample data, though.