From the clues that have emerged, it appears that the dispute is about whether a witness can be forced to answer investigators’ questions. When witnesses refuse to cooperate, prosecutors often go to court to get a judge to send them to jail in order to pressure them to talk. Prosecutors are supposed to exhaust all other investigative avenues before doing this.
A former federal prosecutor argued in an opinion article in October that the dispute could very likely be between Mr. Mueller and President Trump about whether the president had to sit for an interview.
But that does not seem to be the case. The president’s lawyers have said on the record that they are not involved in any litigation with the special counsel’s office, and that the president has not been subpoenaed.