They have taken different public positions on Qatar's treatment by Saudi Arabia and other Gulf States, on Iran's compliance with the nuclear agreement, and now on North Korea.
Tillerson yesterday called a press conference to deny a report he had been close to resigning at one point but was talked out of it by Vice President Mike Pence. He said, "I have never considered leaving this post."
The fact that he would reaffirm his commitment to the job so soon after Trump's outburst on North Korea suggests Tillerson believes he is making enough progress on most of the world problems on his plate. That probably means foreign leaders are listening to him, not his President.
Tillerson outlined the progress he believed he is making on North Korea with economic sanctions, giving credit to colleagues in the administration: Defence Secretary James Mattis, Treasury Secretary Steven Mnuchin and UN Ambassador Nikki Haley.
It is reassuring to know there are such people around Trump. Tillerson's re-commitment to his task yesterday prompted a Republican Senator, Bob Corker, to say, "I think Secretary Tillerson, Secretary Mattis and Chief of Staff [John] Kelly are those people that help separate our country from chaos."
Others who seem to be helping prevent disaster are National Security Adviser HR McMaster and the Chairman of the Joint Chiefs of Staff, General Joseph Dunford.
Right now they are trying to dissuade Trump from reneging on the Iran deal made by President Barack Obama to stop the Islamic republic developing nuclear weapons.
The deal is due for a periodic renewal and Trump has revived his campaign rhetoric against it, prompting Iran to threaten to restart its programme.
Hopefully Iran and countries like it pay more attention to what people such as Tillerson, Mattis, Haley, McMaster and Dunford say and do than to the rhetoric and tweets that come from this odd President.
The world is not accustomed to taking a US President less than seriously, but other countries' leaders and diplomats must be fast learning to do that.
Trump will go on talking as he does to impress the people who voted for him, but so long as he leaves the serious work to the likes of Tillerson, sanity should prevail.