Since it began, there have been two main exponents of Utilitarianism. They are Jeremy Bentham and J S Mill, and both of them base their own individual theories on the principle of utility, which defines something (an act, etc) dependent on if it achieves "the greatest happiness for the greatest number". This makes Utilitarianism a relativistic and consequentialist argument, as it takes into account only the outcome of events rather than the act itself as means to determine whether it is good/right. Also it holds no absolutes - it takes the best interests of the greatest number of people no matter if the way of doing seems morally wrong. Bentham and Mill were both generally harmonious in their understanding that the general happiness of a human being is linked to their personal fulfillment of pleasure. Nevertheless, the two clashed when it came down to the understanding of what true pleasure is, and whether it holds different values under different circumstances.
It was due to this that Bentham started Act Utilitarianism. Bentham thought that situations were to be treated completely differently to any and every other situation, and developed the Hedonistic Calculus as a means of measuring the pleasure and pain of those directly involved in it. The calculus consists of seven aspects which Bentham believed could answer to whether something is pleasurable/painful or not - they are Purity, Remoteness, Richness, Intensity, Certainty, Extend and Duration. It is possible for me to use an example to make this all seem clearer. There are five sadistic guards in a prison who don't like the new inmate and want to give him a roughing up. One can argue that the pain the inmate will suffer is huge (purity) but the calculus is focused on quantity rather than quality. Also, the happiness of the guards will be fulfilled due to their sadistic means of pleasurement (certainty) however, the guards might get caught and sacked which in turn makes them sad in the end, but perhaps they don't then the pleasure of the guards outweighs the pain that the inmate faces and therefore under these guidelines I think that Bentham would say "yeah, go ahead" and allow the bullying and assault to happen.
Bentham's democratic and egalitarianistic approach meant that he believed nobody's pleasures are greater than anyone elses, and that they are all equal so we can't say that they count for more. This meant that Bentham was purely focused on the quantitative side of the pleasure. It was here where Mill and Bentham came to a disagreement, as Mill however focused on the qualitative aspects of the pleasure, famously saying "it is better to be Socrates dissatisfied than a pig satisfied". This meant understanding that there are differences that must be acknowledged between higher and lower pleasures. He thought that higher pleasures consisted of the intellectual aspects of humans rather than the animalistic, such as reading to further your knowledge, listening to fine music and painting art. The aforementioned animalistic pleasures (lower) derive from the physical side of life, such as eating, drinking and indulging in sexual acts. This approach can be seen as elitist by some, which means that full excellence can only be realised by the mature males of the upper class within society - natural amongst the Ancient Greek Philosophers that preceeded Bentham and Mill, such as Socrates, Plato and Aristotle.
As advocator to Rule Utilitarianism, Mill's calculation method again differentiates from Bentham's hedonistic calculus. Rather than Bentham's quantitative approach, Mill looks at it in an alternative way, observing the various implications of the act. Mill's interpretation is that there are general rules within society that should be followed as they create the greatest happiness for the greatest good for all those in society. This at first does seem very logical, but then again it begins to defy the basis on which Utilitarianism's foundations are layed down, which is a relativist and consequentialist theory. And this is where strong and weak rules comes into the frame. Mill never onces says "must" as regards to the rules he would involve as he perceives his judgment upon whether something is good or bad or what should occur within a specific situation, which can be seen as his defence to remaining relativist, however a new term must be enforced to separate his understanding with the likes of a hedonist such as Bentham, hence the term "universalisability".