Some ethical theories are teleological - what is right or wrong depends on the end or outcome of an action - for utlitarians, pleasure, happiness or 'the greatest good'; for Aristotle, 'Eudaimonia'. Other theories are deontological - doing what is right means doing your duty or following the rules - for Kant, the categorical imperative; in Natural Law, the secondary precepts. It is easy to think of teleological theories as relativist and deontological theories as absolutist, but it it not that simple. Apart from Kantian Ethics (thoroughly absolutist and deontological) and Situation Ethics (clearly relativist and teleological), ethics seems to involve an uneasy mix.
Absolutist ethical theories
Kant says that we should act according to maxims that we would want to see as universal laws. These laws are absolutist - we can work them out logically prior to experience; they are not verified through experience (they are known 'a priori').
The consequences of our actions are irrelevant to whether they are right or wrong - evil actions may have unintended good consequences, and someone might act heroically without any guarantee that the consequences will be good. No character quality is absolutely good (good without exception) - for example, it is possible to act kindly but do the wrong thing. The only good thing is a good will that does what is logically the right thing to do.
Natural Law is often described as deontological because, in practice, it leads to a set of rules that people have a duty to follow. These rules are absolutist, because they know of no exception. For example, using contraception to prevent conception is absolutely wrong, regardless of consequences such as the spread of AIDS, unwanted pregnancies etc.
However, Aquinas' Natural Law Theory says we should try to fulfil our God-given purpose. This is teleological, as it is interested in our design or 'end'. The primary precepts - worshipping God, living in an ordered society, reproducing etc. - are teleological: they are the ends to which all our actions should aim. The primary precepts are also absolutist - Aquinas believed we were all made by God with a shared human purpose.
This must not be confused with cultural relativism. Cultural relativism is a very weak moral theory that says things are right and wrong relative to our culture. The theory is easily refuted.
Situation Ethics says that what is right and wrong is relative to the situation. In other words, if you asked "Is it wrong to abort a foetus?" I would ask "Under what circumstances?" Clearly the outcome of my actions is of central importance here. Rules may be useful, but you may need to ignore the rules in order to do the right (loving) thing - the thing that is in the best interests of the people affected.
Theories that can be either absolutist or relativist
When Bentham came up with his Hedonic Calculus, he had developed a theory that allowed you to work out what was right or wrong in any given situation. Euthanasia might lead to the greatest happiness for one person and yet lead to greater unhappiness in another situation. What is right or wrong is relative to the situation, it is whatever has the best consequences (teleological).
Mill, and many since, have adapted Bentham's 'act' utlitarianism, claiming that we need to make laws based on the principle of utility (choose the laws that lead to the greater good) and then follow those laws. This means I have a duty to, for example, tell the truth because it generally leads to greater happiness, even if in this case it will lead to more unhappiness. This is deontological, because it deals with the duty to follow rules. It can be seen as absolutist because there are no exceptions to the rules (if you were allowed to break the rules, this would be act utilitarianism).
Aristotle came up with a list of virtues that we need to acquire, through education and habitually, in order to have a 'Eudaimon' or happy life.
Some modern virtue ethicists, such as Martha Nussbaum, describe Aristotle's theory as absolutist. It is teleological, because it is about the ends or purposes of our actions. However, Aristotle is saying (according to Nussbaum) that certain ends or goals are absolute - it is always good to be honest, kind, courageous etc.
Other modern virtue ethicists say that values change, and different societies hold up different virtues as desirable. What is virtuous, according to MacIntyre, is relative to the context - relative to culture, varying throughout history. Virtue ethics is teleological, focussing on the ends or purposes of our actions. These ends or purposes vary from one society to another throughout time.