What is the difference between Bentham and Mill's Utilitarianism?

Utilitarianism, as it is best understood, is the idea that the best moral action is that which maximises utility. Utility is shorthand for good consequence, this good consequence being the state of highest welfare. For Jeremy Bentham, often considered the father of Utilitarianism, the state of highest welfare is one which maximises human pleasure. Utility then, equates pleasure. He derives this from his genealogy of human drive- a psychological hedonism in which people are subject to 'Two sovereign masters, pain and pleasure.'

John Stewart Mill grew up in the presence of Bentham, and was thus exposed to his thinkings from an early age. For Mill, equating Utilitarianism with pleasure is too parsimonious. If the greatest outcome is truly that which maximises the most pleasure, then a drunk in the gutter wistfully singing the night away might have as high a state of welfare as a child reading Dahl, or a woman who has just given birth. As Bentham claims: "Prejudice apart, the game of push-pin is of equal value to the arts and sciences of music and poetry." In retaliation, Mill refines the concept of Utility to be that consequence which inspires the greatest happiness, as opposed to pleasure. To further this claim, he distinguishes between what he calls higher and lower pleasures, which though may inspire equal pleasure, do not inspire equal happiness. A lower pleasure would be drinking, whereas a higher pleasure might be enjoying music, or a book; "It is better to be Socrates dissatisfied than a fool satisfied."