That's almost correct. What you describe is true for the relationship between CEOs and the board. Or execs and other execs, neither over, nor below them, in the management structure. Those are corporate peers.
For those under your management the relationship is more similar to a military command structure.
Luckily corporate officers can't order you to kill or die. But corporate underlings don't elect their managers. There are many more people being managed, than there are peers.
"But corporate underlings don't elect their managers. There are many more people being managed, than there are peers."
Yes, but. The higher up you go, the higher up a lot of your underlings are, and the more they start to become power brokers in their own right. They report to you, and they will follow orders, but they have their own (strong) agendas, personal and political. Some of them are even rivals, waiting in the wings.
There's a command-and-control structure on a broad level, but the higher you go, the more the pyramid underneath you becomes something like a constituency. (They don't elect you, but they can rebel, they can become unproductive, etc. If you lose their respect, you lose them -- often literally).
For those under your management the relationship is more similar to a military command structure.
Luckily corporate officers can't order you to kill or die. But corporate underlings don't elect their managers. There are many more people being managed, than there are peers.