It may be noticed by the scholar of utilitarianism that the definition of the core of the theory (the principle of utility) has changed over the years, such that the modern version has a number of significant differences from that given by Jeremy Bentham:
"By the principle of utility is meant that principle which approves or disapproves of every action whatsoever, according to the tendency it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words, to promote or to oppose that happiness." 
The modern definition is effectively this:
An action is right if it produces as much or more of an increase in happiness of all affected by it than any alternative action, and wrong if it does not. 
There are a number of differences between the two versions - my thoughts on these differences follow.
The modern version is explicitly to do with right and wrong, and, since utilitarianism is an ethical theory, this would seem to be quite appropriate. Bentham's version is about approval and disapproval, and he seems quite unconcerned with right and wrong - indeed he goes on to say only that
Of an action that is conformable to the principle of utility one may always say either that it is one that ought to be done, or at least that it is not one that ought not to be done. One may say also, that it is right it should be done; at least that it is not wrong it should be done: that it is a right action; at least that it is not a wrong action. When thus interpreted, the words ought, and right and wrong and others of that stamp, have a meaning: when otherwise, they have none.
The apparent ambiguity from Bentham may be to cover the (hypothetical) case where two different actions have exactly equivalent results - Bentham may simply be avoiding the implication that someone ought do two mutually exclusive actions (if so, he uses a very blunt tool to achieve his task - see below). Or, and this is what I am inclined to believe, he just might not be particularly concerned with "right" and "wrong" as they are commonly understood. What I mean by this is that if we say, of two possible different exclusive actions, that one leads to a better state of affairs than the other, then we have said all that needs to be said about them... to go on to say that the first action is right and the second wrong either adds nothing, or it seems to suggest (some deontologists would say implies) that to do the second action is "blameworthy", or "rightfully punishable", or "morally disgusting" or some other phrase indicating a conditioned morality rather than an objective value-maximising one - something that Bentham (and myself) would take care to avoid.
When "right" and "wrong" are stripped of their punishment connotations, I believe they are equivalent to "approval" or "disapproval" by a principle, provided that this principle is justified or warranted by the existence of objective (moral) value.
Part of Bentham's definition is quite obscure: "according to the tendency it appears to have". Appears? Appears to whom? Is the core evaluating principle of utilitarianism subjective? And why be concerned with appearances rather than the actual effects? I think this is a mistake by Bentham, where he has tried to deal with the problem of uncertainty in the wrong section of his theory.
I believe "tendency" is also open to misinterpretation if it is thought to imply that utility involves (only) a class of actions, but this should not happen since it has already been established that it is for any particular action.
Bentham's definition is of utility for some particular party, whereas the modern version is for everyone affected by the action. Neither is really what we mean - we normally consider that Utility considers all (relevant) interests, which is not necessarily what is being said in the modern version (which is potentially subtly misleading). To illustrate: if I am trying to show that the (specific) action I have just performed was the right one, it is not only those who were affected by this action (compared to inaction) whom we must consider, but also all those who would've been affected had I chosen another action instead. I am sure this ambiguity is very common in discussions about Utility, especially those involving an effort to explain utilitarianism in simple (or layman's) terms - though whether or not it actually deceives (that is, that people get the wrong impression) I am not so clear about.
There is really no need for this ambiguity: we can say simply that the right action is simply the one that "maximizes total utility" or "maximizes total happiness" or whatever, we need not say for whom. Any limit we suggest for the scope of our consideration only lengthens the explanation and - as we've seen - introduces the potential for misunderstanding. So let us agree with Bentham when he decided that "the greatest happiness principle" is a better mnemonic for the principle of utility than its predecessor "the greatest happiness for the greatest number" (or the same with "good" substituted for "happiness"). And let us hope that any new definition we produce replaces the current one faster than Bentham's later suggestion effectively replaced his former - for this replacement is, in common usage, yet to occur.
According to Bentham, we are concerned with augmentation and diminuation of happiness, which is to say the changes from the present situation. Utility approves of an action if it makes things better, it disapproves of it if it makes things worse; it approves of one action more than another if that action makes things better than the other.
The modern version is quite different on this point. What is compared against is not the current situation, but the situations that would result from alternative actions. So of two exclusive actions, both of which would increase the level of happiness compared to the present level but by different (positive) amounts, the modern principle would call the better action "right" and the not-so-good "wrong", whereas Bentham's utility would approve of both (but approve of the better one somewhat more) and hold that both actions are right, and ought be done, or at least that they are not wrong, that it is not the case that they ought not be done.
It is surprising to note that neither Bentham's nor the modern version admit of degrees of right and wrong, where it is quite in accordance with common usage to do so: we may usually speak of the right action in a given situation, the alternative actions beings wrong, but it is quite common to speak of one such alternative action being more wrong than another - yet this is quite unaccounted for under these definitions.
There is also a potential stumbling-block for the modern version's comparison: it may be thought that, in choosing between alternative actions, that it implies that there are actually some possible alternative actions in existence. This is a problem if the universe (and particularly psychology) is deterministic, for then it will be the case that there are no possible alternative actions. An agent can only do what he does - to do something else would take a different agent or a different situation, so given the agent and the situation, only one outcome is possible. If determinism is true, the modern version of utility would (thus interpreted) tell us that everything that happens is right.
This problem can be solved only with the acknowledgement that the alternatives under consideration may not actually be possible. In this case, in order to prevent the required analysis of wild fantastical actions, the range must be limited to those actions that can be done, if the agent chooses to do them. That the agent can choose anything other than what he goes on to choose, is (under this interpretation) neither implied nor denied.
In contrast, Bentham's version is clearly unaffected by the presence or absence of non-deterministic free will: it can go on approving or disapproving of actions whether these actions are necessary or not, and whether there are alternatives or not. If what happens is determined solely by the fundamental laws of physics, as they existed at the big bang, then to that extent Bentham's Utility can imply approval or disapproval of the universe as is, has been, and will be. 
Bentham clarifies the position and extent of Utility in various later parts of the text:
"An action then may be said to be conformable to the principle of utility, or, for shortness sake, to utility, (meaning with respect to the community at large) when the tendency it has to augment the happiness of the community is greater than any it has to diminish it."
Notice that, in this expression, utility is concerned with actual - not apparent - tendencies, and that utility is also shown to apply to the effects on the "community at large" (which we can take to mean everyone) rather than some specific party. Also:
"A man may be said to be a partizan of the principle of utility, when the approbation or disapprobation he annexes to any action, or to any measure, is determined by and proportioned to the tendency which he conceives it to have to augment or to diminish the happiness of the community"
Here I think it is reasonable for this approbation to be determined by the "conceived" utility of the action, for this is the judgement of a man - and a man must make his judgements without full knowledge of the relevant facts. If it were defined by actual rather than conceived utility, a utilitarian would not be a utilitarian when he was factually mistaken!
The point about Utility being with regard to the community is also remade here.
There is some potential for confusion in Bentham's definition of the principle of utility, as given at the start of the Introduction to the Principles of Morals and Legislation, but the meaning becomes clearer in later parts of the text.
If we are concerned with stating Utility clearly - in a free-will-agnostic fashion, allowing for degrees of approval or right and wrong, and avoiding the ambiguity on scope already mentioned - then we might define it thus: (in Bentham's style)
or, rather more simply, in Mill's 
"By the principle of utility is meant that principle which approves or disapproves of any action, or of any measure, according and proportioned to the tendency it has to augment or diminish the happiness of the community."
"Actions are right in proportion as they promote happiness, wrong as they produce the reverse of happiness".
1. An Introduction to the Principles of Morals and Legislation, Chapter 1.
2. "The classical utilitarian regards an action as right if it produces as much or more of an increase in happiness of all affected by it than any alternative action, and wrong if it does not." Peter Singer, Practical Ethics 2nd Edition, page 3.
"An action conforms to the principle of utility if and only if its performance will be more productive of pleasure or happiness, or more preventive of pain or unhappiness, than any alternative." The Penguin Dictionary of Philosophy.
"By Utilitarianism is here meant the ethical theory, that the conduct which, under any given circumstances, is objectively right, is that which will produce the greatest amount of happiness on the whole; that is, taking into account all whose happiness is affected by the conduct." Henry Sidgwick, The Methods of Ethics, Book IV Chapter I.
3. The fact that Bentham's Utility does not depend on free will should not be surprising, since Bentham believed in psychological hedonism. What is more surprising is that later utilitarians have modified it to appear to become dependant on free will, yet have not, by and large, rejected psychological hedonism.
4. Somewhat surprisingly, I may say, JSM has a particularly good definition: "The creed which accepts as the foundation of morals, Utility, or the Greatest Happiness Principle, holds that actions are right in proportion as they tend to promote happiness, wrong as they tend to produce the reverse of happiness." John Stuart Mill, Utilitarianism, Chapter 2.