The issue here is restrictive and non-restrictive relative clauses.
In the first sentence, the main point is that the reader enjoyed the stories. The fact that the stories were short is not essential information, so that clause was set off with a comma and introduced by the relative pronoun, which. The second sentence, if it was supposed to have a restrictive relative clause, should have been written like this:
He enjoyed reading the stories that were short.
In this sentence, the meaning is that he only enjoyed the short stories.
It is not an exaggeration to say that these sentences differ significantly; they have completely different meanings.