Authority is not the same as responsibility.
Having authority means that you can pass responsibility onto someone else by commanding them to do the task at hand.
This will then make them accountable for the task and will be in their interests to complete it.
Unlike Leadership, authority often comes with hierarchy or titles.
In an organisation, it is unlikely that line-manager will be able to give orders to the CEO, or make any big decisions for the company. It is often going to be the CEO of a company who holds the most authority, and will be up to them on how much power they want to exert onto their employees.