1 To Put it Simply
In terms of the United States terminology, ‘a governor is the head of a single state’. The executive branch of the state government is headed by the governor. On the other hand, a senator is ‘the representative of the state in the Senate’. Every state has just one governor and two senators, between 1 and 50 representatives within the House.
Senators are a constituent of the federal legislative branch. Therefore, neither one "outranks" the other. So, neither of the two is ranked higher than the other. Having said that, when it comes to state laws and other such state affairs, the governor is at the top of the chain of command in his state. He is answerable to just the President.
2 Who Exactly is a Governor?
The people of a state elect a governor for being the top leader of their state. S/he holds a lot the same powers which a president holds, but only at a street level. S/he can pardon criminals prosecuted by their state, s/he can veto and sign bills that the congress of that state passes. S/he can also appoint people at specific positions.
The governor speaks for the state on issues related to the state. In simpler words, a governor can be called an executive or the CEO of the state, if you see it as a company. You can compare a governor on a state level to the President on the national level as both are head the “executive” branch.
3 Who is a Senator?
A state elects two senators, each of which represents their state's constituency. To do so, they make and vote on laws that are made by congress. There are senators who even serve on several committees. A senator is not an executive but a legislator. They represent the mass of their respective states in the legislative procedure.
As per the Constitution, they are not authorized for executing the laws. You can compare a senator to a representative. However, regardless of the state's population, there are just two senators in every state. Seniority is the criterion while ranking them among themselves. The senior-most senator of the majority party is the President Pro Tempore of the Senate. You can think of the senate as an American version of the council of elders.
4 So, Who is Ranked Higher?
As mentioned earlier, you cannot really compare a senator's rank with that of a governor and vice versa. It is like comparing grape and kiwis. The governors are the heads of their respective state governments, while the senators deal with the federal government. Usually, a governor of a populous and wealthy state would be at a more prestigious status than a junior senator of a state with small clout. Similarly, a senator from any U.S. state would, of course, be at a more prestigious level than the governor of a sparsely populated and impoverished state.
If you bring the Constitution into the picture, you could debate that as the governor is the top-most authority in a state, s/he would be at a higher rank. Likewise, when a senator leaves office prematurely, the authority of appointing a replacement/substitute until the next election lies with the governor. Keeping all this in mind, governors generally turn out to be better presidents as they hold executive experience in the state-level government.
However, this does not mean that a senator would not be successful in being a good executive. It is just that a senator’s executive experience can nowhere be in comparison to that of the governor.
5 What is the Senate?
A deliberative assembly, usually the chamber or upper house of the bicameral legislature, is known as a senate. It gets its name from the good old Roman Senate. It is derived from the Latin word 'senate' and is called an assembly of the 'seniors'. The Latin word for ‘seniors’ is ‘senex’, meaning an “old man” or “the elder”. Therefore, the senators are considered as more experienced and wiser members of the ruling class of society. Many nations consist of an assembly called a senate and are comprised of senators who can be appointed, elected, have inherited a title, or acquired memberships through other methods; it depends on the country.
Typically, modern senates serve for providing an upper house of "sober second thought" for considering the legislation passed by the lower house. The members of the lower house, as mentioned earlier, are generally elected. Most of the senates have asymmetrical powers and duties compared to their respective lower houses. It means that they possess special duties, for instance, for filling important political positioning or passing special laws. Many senates conversely have limited powers to stop or change bills under efforts and consideration of vetoing or stalling a bill might be bypassed by the lower house or other branches of government. (See Why is Government Necessary?)
6 Flipping the Pages of History
Many governors and senators in their term aspire on holding the office of the President of the United States. But, the Constitution does not mention anything that states that the President has to be a senator or a governor. It just states that the President has to be a minimum of 35 years of age and a citizen of the United States. There is no mention of experience. However, the masses believe that a person with military and/or governmental experience is better than the one with no such experience. It is the reason behind the proliferation of governors.
As Governors possess a lot of the same powers (on a state level) as the President, the United States has elected a plethora of governors to the President position. The names are Jimmy Carter, Bill Clinton as well as George W. Bush. Even Senators have been presidents. JFK and Richard Nixon (after being VP) would be the examples. Dwight Eisenhower as well as George Washington were military leaders and went on to become presidents.