Real power in the senate is in the hands of the Majority leader
The Vice President of the United States is the official Senate President, and when the Vice President is not present, the President pro tempore assumes that role. But in practice, unless a tied vote is anticipated, the Vice President hardly ever enters the Senate, much less actually preside over the body, and the President pro tempore has devolved into a ceremonial position devoid of any real authority.
In accordance with Senate rules, the Presiding Officer of the day gives the Majority Leader priority in obtaining recognition to speak on the Senate floor and they decide which senators will be allowed to speak. This is because the Majority Leader is seen as the de facto leader of the Senate, especially in modern times.
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