What is the relationship between a state and a municipality within that state?

So we'll start be explaining what a state and a municipality are. A state is pretty commonly known. Its a division of land in the US which its own government. A municipality is a city within a state. So lets explain the relationship. This changes depending on the state. You could think of it as a chain of command with the governor on top. He controls the entire state's budget. This has an effect on every city within the state.