Apparently Mueller took exception to Barr's 4 page letter that provided the Mueller Dossier's principal conclusions. Barr initially issued that letter shortly after receiving the Dossier--he wanted Barr to also release the executive summaries from the Dossier. Barr's position was simple: he issued his four page letter to fulfill the reporting requirements in the regulations. He did not agree with Mueller's idea of a partial release of the Dossier, preferring to release the entire document as a whole, with necessary redactions. That was exactly what Barr did.
Here is a key passage from the WaPo article:
A day after Mueller sent his letter to Barr, the two men spoke by phone for about 15 minutes, according to law enforcement officials.
In that call, Mueller said he was concerned that media coverage of the obstruction investigation was misguided and creating public misunderstandings about the office’s work, according to Justice Department officials. Mueller did not express similar concerns about the public discussion of the investigation of Russia’s election interference, the officials said. Barr has testified previously he did not know whether Mueller supported his conclusion on obstruction.
When Barr pressed Mueller on whether he thought Barr’s memo to Congress was inaccurate, Mueller said he did not but felt that the media coverage of it was misinterpreting the investigation, officials said.
In their call, Barr also took issue with Mueller calling his memo a “summary,” saying he had never intended to summarize the voluminous report, but instead provide an account of its top conclusions, officials said.