Bentham devised the utilitarian theory. He claimed, ourselves, as humans are hedonists, we seek pleasure and avoid pain.
He claimed that the principle of utilitarianism is that right or wrong of an action is determined by its usefullness, or equally its uselessness.
Thus he devised the hedonic calculus, which weighs up the pain and pleasure and the utility of an action.
People that follow this theory maintain the belief that the good action is the one which leads to the greatest good.
However this theory has been critiscised and claimed to be impractical as you have to equally weigh up every action before partaking it.
John Stuart Mill
JSM focused primarily on qualitative pleasures and claimed that pleasures of the mind are a priority to those of the body.
He also claimed that higher pleasures are related to lower pleasures but the name holds the priority.
One of his most famous quotes was "It is beter to be a human disatisfied than a pig satisfied. It is better to be Socrates dissatisfied than a fool satisfied."
Rule utilitarianists establish the best overall rule by determining the course of action which leads to the greatest result.
Rule utilitarianism overcomes some of the difficulties that act utilitarianism present.
It can still be twisted so it looks like it promotes schemes such as slavery or it can just be genuinely misconcepted.
What matters in this type is the satisfaction of all affected interests.
Preference, hence the name believes in a classless society and that an individual cannot be sacrificed for another.
Singer, especially believes that people should live on the deliberate general principles rather than consider every action.