A story is told. And there is another version of the story. I would like to mention in the continuation of the sentence what's the difference compared to the above mentioned story, expressing that is not a big difference (hence the word "only"). And one more thing: inserting a "basically" too. I think "The other version shows basically only such a difference" is even more awkward.
Yes, it's a very evident answer, and I wasn't precise enough. The difference is not only one thing but more, though even adding them it's a slight difference. However, I think that then I couldn't say "the only difference," like this: "In the other version, the only difference is that he is a doctor and he gets to know Jane in a shop, not in a park. Then shall I say "the few pieces of differences
eg There are two versions of the story. In one, Tom is a lawyer. In the other version, the only differences are that he is a doctor and thathe meets Jane in a shop.