If you're unsure of a question of philosophy, the Stanford Encyclopedia of Philosophy is usually the best place to consult first. Its history of utilitarianism article says that
Though there are many varieties of the view discussed, utilitarianism is generally held to be the view that the morally right action is the action that produces the most good. There are many ways to spell out this general claim. One thing to note is that the theory is a form of consequentialism: the right action is understood entirely in terms of consequences produced. What distinguishes utilitarianism from egoism has to do with the scope of the relevant consequences. On the utilitarian view one ought to maximize the overall good — that is, consider the good of others as well as one's own good.
The Classical Utilitarians, Jeremy Bentham and John Stuart Mill, identified the good with pleasure, so, like Epicurus, were hedonists about value. They also held that we ought to maximize the good, that is, bring about ‘the greatest amount of good for the greatest number’.
Utilitarianism is also distinguished by impartiality and agent-neutrality. Everyone's happiness counts the same. When one maximizes the good, it is the good impartially considered. My good counts for no more than anyone else's good. Further, the reason I have to promote the overall good is the same reason anyone else has to so promote the good. It is not peculiar to me.
Note the last paragraph in particular. Utilitarianism is agent-neutral: while it does take your utility function into account, it gives it no more weight than anybody else's.
The "general utilitarianism" that you mention is mostly just "having a utility function", not "utilitarianism" - utility functions might in principle be used to implement ethical theories quite different from utilitarianism. This is a somewhat common confusion on LW (one which I've been guilty of myself, at times). I think it has to do with the Sequences sometimes conflating the two.
EDIT: Also, in SEP's Consequentialism article:
Since classic utilitarianism reduces all morally relevant factors (Kagan 1998, 17–22) to consequences, it might appear simple. However, classic utilitarianism is actually a complex combination of many distinct claims, including the following claims about the moral rightness of acts:
Consequentialism = whether an act is morally right depends only on consequences (as opposed to the circumstances or the intrinsic nature of the act or anything that happens before the act).
Actual Consequentialism = whether an act is morally right depends only on the actual consequences (as opposed to foreseen, foreseeable, intended, or likely consequences).
Direct Consequentialism = whether an act is morally right depends only on the consequences of that act itself (as opposed to the consequences of the agent's motive, of a rule or practice that covers other acts of the same kind, and so on).
Evaluative Consequentialism = moral rightness depends only on the value of the consequences (as opposed to non-evaluative features of the consequences).
Hedonism = the value of the consequences depends only on the pleasures and pains in the consequences (as opposed to other goods, such as freedom, knowledge, life, and so on).
Maximizing Consequentialism = moral rightness depends only on which consequences are best (as opposed to merely satisfactory or an improvement over the status quo).
Aggregative Consequentialism = which consequences are best is some function of the values of parts of those consequences (as opposed to rankings of whole worlds or sets of consequences).
Total Consequentialism = moral rightness depends only on the total net good in the consequences (as opposed to the average net good per person).
Universal Consequentialism = moral rightness depends on the consequences for all people or sentient beings (as opposed to only the individual agent, members of the individual's society, present people, or any other limited group).
Equal Consideration = in determining moral rightness, benefits to one person matter just as much as similar benefits to any other person (= all who count count equally).
Agent-neutrality = whether some consequences are better than others does not depend on whether the consequences are evaluated from the perspective of the agent (as opposed to an observer).
When someone complains that utilitarianism1 leads to the dust speck paradox or the trolley-car problem, I tell them that's a feature, not a bug. I'm not ready to say that respecting the utility monster is also a feature of utilitarianism, but it is what most people everywhere have always done. A model that doesn't allow for utility monsters can't model human behavior, and certainly shouldn't provoke indignant responses from philosophers who keep right on respecting their own utility monsters.
The utility monster is a creature that is somehow more capable of experiencing pleasure (or positive utility) than all others combined. Most people consider sacrificing everyone else's small utilities for the benefits of this monster to be repugnant.
Let's suppose the utility monster is a utility monster because it has a more highly-developed brain capable of making finer discriminations, higher-level abstractions, and more associations than all the lesser minds around it. Does that make it less repugnant? (If so, I lose you here. I invite you to post a comment explaining why utility-monster-by-smartness is an exception.) Suppose we have one utility monster and one million others. Everything we do, we do for the one utility monster. Repugnant?
Multiply by nine billion. We now have nine billion utility monsters and 9x1015 others. Still repugnant?
Yet these same enlightened, democratic societies whose philosophers decry the utility monster give approximately zero weight to the well-being of non-humans. We might try not to drive a species extinct, but when contemplating a new hydroelectric dam, nobody adds up the disutility to all the squirrels in the valley to be flooded.
If you believe the utility monster is a problem with utilitarianism, how do you take into account the well-being of squirrels? How about ants? Worms? Bacteria? You've gone to 1015 others just with ants.2 Maybe 1020 with nematodes.
"But humans are different!" our anti-utilitarian complains. "They're so much more intelligent and emotionally complex than nematodes that it would be repugnant to wipe out all humans to save any number of nematodes."
Well, that's what a real utility monster looks like.
The same people who believe this then turn around and say there's a problem with utilitarianism because (when unpacked into a plausible real-life example) it might kill all the nematodes to save one human. Given their beliefs, they should complain about the opposite "problem": For a sufficient number of nematodes, an instantiation of utilitarianism might say not to kill all the nematodes to save one human.
1. I use the term in a very general way, meaning any action selection system that uses a utility function—which in practice means any rational, deterministic action selection system in which action preferences are well-ordered.
2. This recent attempt to estimate the number of different living beings of different kinds gives some numbers. The web has many pages claiming there are 1015 ants, but I haven't found a citation of any original source.