I haven't read Luna Oi's translation in a while, but essentially the difference is:

Dialectical materialism: How subjective (human) consciousness and the objective material world interact with one another.

Materialist dialectics: Dialectical relationships from a materialist perspective.

So there's a dialectical relationship between a book that's resting on a table and a table that's holding the book up. This is materialist dialectics because the book and the table exist within the context of each other and have a contradiction (force of gravity pushes the book down on the table while the normal force pushes the book up), but it's not dialectical materialism because a human isn't involved.

What gets tricky is that just like the table and book exists within a context of each other, they also exist within the context of the objective material world, and this objective material world is shaped by human consciousness through the action of humans. Someone made that table, someone made that book, and someone placed them in such a way that the book is on top of the table, which means there's a dialectical relationship with the book and table on one side and the humans who made it so on the other side. Now, you have to use dialectical materialism to fully explain this.

In a way, materialist dialectics by itself is insufficient but naturally leads to dialectical materialism anyways.