Universalism: Utilitarianism holds that morality is universal, that the same moral standards apply to all people and all situations. The standards that define what is right are the same for me and you, regardless of who we are. This isn't particularly controversial, because most ethical philosophies since the Enlightenment have been universalist. An important consequence of this view is that the utility of all people is important, and is in fact assumed to be equally important. This means that Utilitarianism is an egalitarian philosophy, holding that all people should count equally. It should be noted, however, that many people believe that if someone is friend or family, you should regard their welfare as morally more important than that of others.
Consequentialism: Utilitarianism holds that what matters, morally speaking, are the consequences of actions. A technical word for this is "Teleological". What this means is that, to Utilitarians, it is the real world results of something that are good or bad, not something intrinsic to the action itself. For example, telling a lie would be bad if it produced bad consequences (which lies usually do). It would not be wrong just because it is a lie. This view is quite controversial, and the main opponents of Consequentialists are the people who support rights theories. The technical word for the positions opposed to consequentialism is "Deontological". These view may hold that, for example, telling a lie is always wrong because all lies are wrong, regardless of what their effects are. Rights theorists support the idea of "natural rights", which are rights that it is inherently wrong to violate regardless of the consequences.
Welfarism: Utilitarianism's definition of what is good is a welfarist definition. Good consequences are those which increase the well-being of specific people. This well-being is subjective. The exact conception of welfare varies, but it is always something like happiness, satisfaction of preferences, attainment of goals, or something else like that. What is good is the welfare of people, and the welfare of people depends on whether each person as an individual is living a good life from their perspective. A belief opposed to welfarism would be the idea that something is a good consequence regardless of whether or not people desire it. For example, one such belief would be that fairness is inherently good even in situations where nobody involved cares about it or benefits by it in any way.
Aggregation: Utilitarianism is an aggregative philosophy, meaning that its conception of individual goods allows them to be summed up into a single measure of overall good. Utilitarianism holds that the welfare (utility) of different people can be compared, and thus summed up into a total which describes the overall welfare of all people. Aggregation is controversial, because many people believe that the welfare of different people cannot even in principle be compared.
Maximization: Utilitarianism is the most famous maximizing philosophy. A maximizing philosophy is one which says that, whatever is good, it is best to have as much of that good as possible. In the case of Utilitarianism, the best course of action is the one which brings about the highest level of welfare. Not all philosophies are maximizing. Some non-consequentialist philosophers (Kant is probably the most famous) held that it is wrong to do something bad even if that will reduce the total amount of bad things in the world. Some consequentialist, welfarist philosophers believe that welfare should be equalized between people, rather than being maximized.
Universalism: All Utilitarians are universalists.
Consequentialism: There are two major views of how consequences matter, Act Utilitarianism and Rule Utilitarianism. Act Utilitarianism, the original and most common position, holds that the rightness of any action depends on the consequences of that specific action. Rule Utilitarianism holds that the rightness of any action depends on whether or not that action follows a universal rule which would have good consequences if everyone followed it. Under Act Utilitarianism, the rightness of actions is evaluated on a case by case basis, and things such as rules and laws are only present if they have practical usefulness. Under Rule Utilitarianism, the utility of rules rather than actions is evaluated, and all actions should conform to the rules with the highest utility. A rare third variant, Ideal Utilitarianism, holds that the consequences which matter may include how well actions conform to abstract principles or ideals. This is not properly Utilitarianism at all, however, because it violates Welfarism.
Welfarism: One of the larger disagreements in Utilitarianism is exactly what welfare is. The oldest variant is Hedonistic (or Benthamite) Utilitarianism, which holds that welfare is equivalent to the presence of pleasure and the absence of pain. Hedonistic Utilitarians define utility solely according to one's state of pleasure and pain, regardless of the causes of that state. A newer and now more common variant, Preference Utilitarianism, defines utility as the degree of satisfaction of one's preferences. To a preference Utilitarian, if someone prefers for something to happen, then that something increases their utility even if it does not produce pleasure or remove pain. There is disagreement about exactly what preferences are, and opinions on the matter fall into two main camps. Those who believe in expressed preferences think that you prefer something if and only if you choose it over the alternatives when the occasion comes. Those who believe in informed preferences believe that people do not always choose what would be best for them. They hold that preferences are what someone would choose over the alternatives given hindsight, or given ideal knowledge of all the alternatives, or given ideal powers of reasoning. A rare third variant, Negative Utilitarianism, holds that utility is defined solely by the absence of bad things, such as pain (and thus that the presence of good things does not effect it).
Aggregation: There is one difference of opinion between Utilitarians on the question of exactly how individual utilities should be aggregated into overall utility. Some believe that they should maximize total utility, so that adding more people to the population, which would also add their utilities to the total, would in general be a good thing. A consequence of maximizing total utility in this way is that a poorly off, but truly huge, population would be preferable to a well off but significantly smaller population. Others believe that they should maximize the average utility of the population. They believe that the point of egalitarianism is to make tradeoffs between the utility of different people on an equal basis, so that the average utility of the people concerned should be maximized. According to them, it is missing the point to say that adding more people is an improvement, even if it decreases the welfare of the current members of the population.
Maximization: There are two different debates among Utilitarians that are related to the issue of maximization. The first is about whether actions should be chosen according to whether they maximize expected utility (the amount of utility that is predicted to result, given the unpredictability of the world), or according to whether they maximize the actual utility that results after the fact. While maximizing the actual utility is what produces the best results, the fact is that only expected utility can be maximized without the ability to perfectly predict the future. For this reason, many Utilitarians explicitly say that the best course of action is to maximize expected utility, because this more realistic definition is easier to work with. The second debate is over Direct versus Indirect Utilitarianism. Direct Utilitarians believe that in order to maximize utility, people and organizations should explicitly try to maximize Utility. According to them, Utilitarianism demands that we consider the various courses of action according to how much utility they will produce, and pick the one which maximizes it. Indirect Utilitarians believe that calculating utility is not something people are very good at on a day to day basis. According to them, it may be most effective if people follow laws and rules of thumb which are effective in practice. This will often maximize utility more effectively than if people always explicitly tried to calculate utility, because people are not very good at trying to calculate the utility of every action they take.
Normative: Normative ideas are theoretical ideals. A normative idea sets out a theory of how things would be if they were perfect. Normative ideas are useful because they set out a standard against which to measure everything else. Nothing in the real world is perfect, but the ideal functions as a yardstick to tell us just how good it is. Normative ideas are not supposed to be realistic, or to describe something that we might actually achieve. They are perfection, and true perfection is beyond our reach.
Descriptive: Descriptive ideas are empirical reality. A descriptive idea attempts to explain or describe reality as it actually is. Descriptive ideas are useful because they establish our theoretical and practical understanding of how the world works, what it is like, and why. This allows us to deal with the real world from a position of knowledge and awareness of it. Descriptive ideas are not supposed to tell us how things should be, or how we should change them. They are reality with all its warts.
Prescriptive: Prescriptive ideas are suggestions for practical improvements. Such an idea prescribes actions or policies which are likely to succeed in improving the real world. Prescriptive ideas are useful because only they tell us how we should act in practice so as to improve things. Descriptive ideas tell us how things are, but not how they should be. Normative ideas establish ideals to work toward, but they are not in themselves practically achievable. A prescriptive idea takes into account descriptive reality, and tells us what we can do to move closer to the normative ideal. Prescriptive ideas are not necessarily similar to normative ideals, because aiming to bring about an ideal in the most straightforward or direct manner may not be the most effective way to get nearer to it.