According to act utilitarianism, the measure of the value of an act is the amount by which it increases happiness to a person. If the act produces much happiness as compared to any other act then the act is morally right. To understand the term act utilitarianism, compare the consequences of doing a charity work and the consequences of watching TV at home. A person can generate more happiness by doing charity work as compared to watching TV. In this situation according to act utilitarianism, the right thing for a person is to do charity work as compared to watching TV because charity work will generate more happiness.
Problem with Act utilitarianism
Though there is some criticism on this theory because for some people the act of torturing and enslavement is a source of happiness and this theory allows these act morally. This act according to some critics justifies crime.
Another issue about this act is that how will the happiness be calculated. This is always difficult to find out that which act will generate more happiness.
Rule utilitarianism
Rule utilitarianism is a form of utilitarianism that says an action is correct only if it conforms to a rule that leads to the greatest good and generates happiness. For rule utilitarians, the amount of good brought about when followed determines its rightness.  Rule utilitarians argue that following some rules leads to the greatest good will, and this will have have better consequences overall.
Problem with rule utilitarianism
In some cases  breaking the rule produces more utility so people tend to break rules. In this case sub-rules should be added that can handle such cases.
Difference between Act utilitarianism and Rule utilitarianism
These two forms of utilitarianism differ from each other. Act utilitarianism is based on consequences while rule utilitarianism is based on rules. Act utilitarianism sees the consequence of an action in itself whereas rule utilitarianism sees the consequences as if it will be repeated all over again. Act utilitarianism before choosing an act first looks into the consequences then the one with the better consequence is selected while rule utilitarianism looks first into the consequences of choosing what rule to follow. The more correct choice is the rule that generates the greatest utility or happiness.
According to the theories, act utilitarianism is the belief that it is correct to break a rule as long as it brings a greater good and happiness, while Rule utilitarianism is a belief that even if a rule does not bring a greater good, breaking it will not bring a good either.
In Act Utilitarianism the value of an action is not judged in terms of laws. Instead it states that when the actions benefit the most people they are moral. For example, a person might say “it is moral to murder someone if they are a danger to society.” even though the law is present against murder.
Rule utilitarianism states that an action is correct only in reference to a rule. It measures the amount of ‘good’ an individual action does by acting according to a law. For example, taking the same example of murder, a person might say  “Murder is wrong according to the law and if everyone follows the law, no one will have to be afraid of being murdered and we can be in public and private spaces without any fear.”

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Conclusion
Act utilitarianism states that an act is correct if the act produces much happiness as compared to any other act. Act utilitarianism sees the consequence of an action in itself . There is some criticism on this theory because for some people the act of torturing and enslavement is a source of happiness and this theory allows these act morally.
Rule utilitarianism is a form of utilitarianism that says an action is correct only if it conforms to a rule that leads to the greatest good and generates happiness. There is some criticism on this theory because in some cases  breaking the rule produces more utility so people tend to break rules.
The difference between these two acts is that act utilitarianism sees the consequence of an action in itself whereas rule utilitarianism sees the consequences as if it will be repeated all over again. Act utilitarianism is the belief that it is correct to break a rule as long as it brings a greater good and happiness, while Rule utilitarianism is a belief that even if a rule does not bring a greater good, breaking it will not bring a good either.