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Lord Twig
Maybe this will serve as an example of the difference between Leadership and Authority - one that doesn't get into the more philosophical or intangible aspects of Leadership.
Air Force CSAR (combat search and rescue) helicopter crews usually consist of four members (not counting PJ's - Pararescue Jumpmen - which are more interchangeable between flight crews). Those crew members are: Pilot (officer), Copilot (officer), Flight Engineer (enlisted), Gunner (enlisted).
There are obviously levels of authority involved, with the Pilot ultimately responsible for the aircraft and crew, and most likely the senior ranking crew member. However, every good crew treats everybody as equal members of the team, with equally valued inputs and equal authority to call a no-go. Many crews also make a point of stating this during their pre-flight brief as a reminder before every flight.
Every member of the crew, along with their specific in-flight responsibilities, also functions as a spotter. Helicopters fly at relatively low altitudes and can encounter a lot of hazards as a result. You can be certain that if the Flight-engineer on the right side of the helicopter sees a hazard (be it a power line, tree, or enemy), and directs "Break Left" over the com, the Pilot is not going to think
"Hey, he's not in charge here! Who the hell does he think he is?!?!"
What the Pilot is going to do is break left - hard and immediately.
That's really no different from what a Warlord does.
The Fighter is a specialist in personal combat. The Warlord is a specialist in seeing the big picture.
Let's take the Battle Master's
Commander's Strike as an example.
It says:
"When you take the attack action on your turn, you can forgo one of your attacks and use a bonus action to direct one of your companions to strike. When you do so, choose a friendly creature who can see or hear you and expend one superiority die. That creature can immediately use its reaction to make one weapon attack, adding the superiority die to the attack's damage roll."
Direct is one of those words that can mean an authoritative order or just guidance.
Narratively it could be that the Warlord, with the benefit of distance giving a wider perspective, sees that the foe the Fighter is engaged with drops his guard just a tad after most parries. He also notices that the foe half-steps with his left foot every time he drops that guard. So when the Warlord sees it happening again, he let's the Fighter know by yelling "Andros...Stop-Cut Octave...Now!"
Is the Fighter under any obligation to do what the Warlord says? No.
Is the Fighter a subordinate or "animal companion" of the Warlord? Of course not.
Will the Fighter benefit by heeding the Warlord's guidance? Most Definitely!
That is Leadership, not Authority.