Who rules who?

In England - England is ruled by a monarchy. Kings and Queens. There is a prime minister too who is involved with the politics also.
In America there is a government. That government is primarily ruled by the president of the United states of America.
Why the difference? I'm sure there is a long story about it. And most people seem to be extremely interested in this. I know when I went to visit England recently, I had a few people who asked me about the president and the decisions he was making. People tend to attribute all the decisions made to this 'one guy' - the one ruler.
My limited political knowledge prevents me from elaborating further. Just an observation... so who rules who?