At this point in our political discourse, the terms "liberal" and "conservative" are meaningless labels that for historical reasons are applied to what they are applied to. They have no reliable relationship to their historical meanings, or the meanings used in other countries for the same terms.
"Liberal" and "conservative", in literal modern non-political usage, both refer to a resource allocation strategy; a "liberal" strategy allocates a lot of resources to something, while a "conservative" strategy tries to use as few resources as possible. While there is some correlation between these meanings economically, it is not one that will usefully help you to determine if a given policy is usually considered liberal or conservative. "Cutting the military budget" is a common liberal position, while a conservative might want to increase money for the space program.
In this sense, the closest modern conservatives are the Libertarian party, and the closest liberals are campaigning politicians of either major party. (Lately both parties are acting disturbingly resource-liberal without regard for possible consequences; it's definately an argument over how deeply we will go into debt and who gets the payout, rather than whether we should be in debt at all.)
In much earlier times, a "conservative" might be one trying to defend the old traditions, while a "liberal" is one embracing change and willing to try new things. This is the same "liberal" we have in the term "liberal education". (The Christian terms used in that essay should be considered authentic; at the time this term was created I suspect few people would have major disagreements with the tone of that link.) There is obviously a correlation here too, but again, it isn't so strong that it is useful to fully determine what a given stance will be considered. Both parties have significant conservative and liberal positions; "preserving Affirmative Action", a fundamentally Conservative action given that Affirmative Action already exists, is considered a Liberal cause, while the "pre-emptive war" doctrine, fundamentally Liberal in nature, is considered Conservative... well, actually it is considered neo-Conservative, which along with clearly showing the continued mutation of these terms, is also an oxymoron by this definition.
In modern times, Conservative and Liberal are a vague coalition of interests and positions. Often they are loosely correlated to the major meta-coalitions, with the Republicans being the conservatives and the Democrats the liberals, but there are many exceptions even then. Worst of all, they are commonly used today relative to the speaker; the speaker will decide they are one or the other and if you disagree with them, you must be the opposite. There are a few "core issues" this doesn't usually apply to, but for things on the fuzzy fringe this is often how it works, and both of the meta-coalitions use this to great rhetorical effect.
Other countries use the terms, and while I can't make an exhaustive list of them, I can certainly say the American use of the terms bears no particular relationship with them, either. (Relationships, yes, but nothing strong enough to be predictive.)
In the absence of a definition, these terms are useless in modern times, as evidenced in the previous paragraph by the way people can use their inherent fuzziness to score points by labeling people almost willy-nilly. Every time I use the terms now, I define them. Sometimes, I will define them as "the fuzzy things we all know them to be", and that is OK, as long as one does not subsequently rely on the definitions of either word to make a point about Conservatives or Liberals.
Incidentally, with very similar logic you can show that the terms "Republican" and "Democrat" have very little meaning, especially in light of myths 1 and 2. I may may claim I am a Republican, but that doesn't mean I support them across the board, nor does it mean I will be Republican in ten years; both the meta-coalitions and I may drift until I decide that I better match the Democrats. Any time you see anybody using logic of the form "X is a Republican" -> "Republicans believes something stupid Y, so therefore X does too" -> "X is Stupid", your BS detectors should go off. Both meta-coalitions cater to a wide variety of moonbats, and you would be hard pressed to find someone who totally agrees with all of either meta-coalition.
The confusion above leads us to two logical/argument fallacies:
Arguing From The Label #
Once you have established somehow that a person is a Liberal or a Republican or whateven, it is inappropriate to then reason from the label to attempt to either derive some other belief the person has, or, worse, to attempt to tar them by association with some other person who happens to have the same label.
This is not a new fallacy; technically it a composite of Division (attributing attributes to a part that are properly attributed to the whole only), Wrong Direction (people's beliefs cause the labels, the labels do not cause the beliefs), and in some cases Guilt by Association. However, it comes up often enough to bear special mentioning (and a link target!).
A person's beliefs need not even be coherent or consistent. Incoherency or inconsistency is undesirable, and indicates that they are almost certainly false or incomplete, but those aren't constraints either; people believe false and incomplete things all the time. In fact, it can't be avoided. (As a concrete example, few people believe true things about physics when it comes right down to it, believing things that are at the very least incomplete and almost certainly at least somewhat false. But somehow, they manage to keep believing these things, and one can argue that for most people the requisite effort to believe true things is largely a waste anyhow.)
This fallacy is especially poignant when someone, in their zeal to label somebody else, they get it wrong, usually either by using some sort of touchstone issue, especially in relation to their own beliefs and a black/white view of rightness that is increasingly in vogue amoung a certain strident part of the far left.
People are people, and may freely believe as they wish and act as they choose with relatively few true constraints on them.
Label Equivocation #
Label equivocation is a special case of equivocation, a word used with multiple meanings, again worthy of special mention since this exact equivocation occurs so often. This occurs when non-complementary definitions of the above terms are used in opposition to each other, such as pitting economic liberalism against social conservatism, and arguing from one side that you should or should not support the other. Arguments about economic liberalism have little or nothing to do with social conservatism, no matter how you define those two terms within reason. Whenever these labels are used, they should be carefully defined.
(This is #5 in the Government Myths series.)