Consequentialism
A major categorization of ethical theory is the distinguishing of consequentialist theories versus deontological theories. Theories of consequentialism are united in the belief that the moral value of actions ought to be determined based on the outcomes of those actions. Utilitarianism is often touted as the flagship moral theory of consequentialism. (Deontological theories, in contrast, ground the moral value of actions in the intentions motivating them.)
Practicality
One issue of moral theory is the matter of how useful it is in real life. The theory of utilitarianism was designed, in large part, as a practical guide to evaluate moral dilemmas and execute informed actions. Compared with Kant's categorical imperative, for example, some argue that utilitarianism seems less idealistic exactly because it better conforms to the nature of the real world.
Democracy
It is no coincidence that Mill penned both this theory of utilitarianism and a theory of representative, democratic government. A large part of what made Mill's views so progressive was that it places value in the pleasures and pains of every person, as opposed to placing the ruling class above the rest of society.
Hedonism
Mill's utilitarian theory is a derivative of the broader philosophical doctrine known as hedonism. Hedonism holds that all moral judgments, societal constructs, and psychology are ultimately grounded in considerations of pleasure and pain.
Classes of Pleasures
A major distinction between Mill's utilitarianism and Bentham's utilitarianism is that Mill articulates different classes of pleasures; that is, there are some pleasures of a higher, intellectual value, and there are baser pleasures, the sort of which we share with animals. In so doing, Mill's calculus of the morality of actions ends up being more sensitive to specific types of pleasure than Bentham's.
Appeal to Mathematics
Consequentialist theories of morality are typified by their a posteriori (grounded in experienced evidence) valuation of actions; we ought therefore to note that utilitarianism is also grounded in a priori (independent of experience) principles, though not in the way deontological theories rely on a priori knowledge. The a priori strength of utilitarianism is in its mathematical analysis of morality; by employing the principles of math to balance pleasure and pain, Mill attempts to construct a theory that objectively vets the moral content of actions. The difficulty, of course, which Mill endeavors to overcome, is establishing metrics of pleasure and pain that can function similarly to numbers.
Moral Decidability
Smith's theory reflects a philosophical belief that actions have real moral weight, which can be evaluated using reason. This evaluation, in his case, consists of weighing the pleasure effected by the action against potential pain inflicted by it.
Prescriptivity
Like many types of moral theory, utilitarianism is a guide of how one ought to act. Smith posits that there is an ethically correct way to conduct one's life based on basic principles of pleasure and pain, and seeks to articulate the precise method by which one may adhere to them.
Subjectivity vs. Objectivity
Mill seeks in utilitarianism to distinguish between the objective - that which is good without reference to one's perspective - and the subjective - that which is understood through one's experiential lens. Because utilitarianism derives goodness from the experiential notions of pleasure and pain, this is a key distinction to track.
Moral Proof
Mill follows in the tradition of his contemporary moral theorists by arguing that the proof of a moral theory is a feeling of its cohering with our intuitions about what is naturally the case; yet he seeks to go beyond a simplistic account of these intuitions by stressing that moral theory requires a rational account to which our intellect assents.
