Each society is allowed to have its own system of governance (democracy, monarchy, freehold, etc.) over whatever space it owns, ranging from a small state, several continents or oceans (Naboo/Ryloth), a whole planet, even an entire star system (Mandalore).
The ruler (governer/king/queen/dictator/minister/president) decides how that government acquires resources, how it uses those resources, etc.
The senator is only a representative for that government to the Galaxy. They work for the Republic/Empire and decide Galaxy-wide law, but have no say in the laws of their gov't.
The moff is like a Vassal to the Emperor, who owns the Galaxy. He/she is usually given an entire sector (made up of hundreds of star systems) to oversee. Since they represent the Empire, they can barge into any government at any time and do as they please.
You could argue that the senators decide what powers the moffs have, but in the case of a moff deciding to march soldiers into a smaller gov., the senator of that gov. (or even the ruler) can't immediately do anything about it.
A Moff controls that world, along with all the other worlds in their designated sector of space. They also control all of the military assets in their sector.
A Governor only controls that one world and its assets. It is primarily a political position, as they have no real military power unless permitted by a higher ranking officiant... And if their world becomes militarized for whatever reason, a Governor falls into the chain of command, and becomes subordinate to certain military officers(that's why Thrawn outranked Pryce on Lothal, for example.)
A Senator is essentially just that world's political 'voice'. Any issues or requests the Governor might have are brought before the Senate by the Senator. They would be the next in command of that world if something happened to the Governor.
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."