When we talk about morality or ethics in the prescriptive sense, we rarely if ever think of it as the property of an individual. Obviously, it's common enough in colloquial speech to say something like "That's against my moral code," but philosophically speaking phrases like 'my morality' or 'his ethics' are more or less meaningless. In philosophical ethics, the distinction we are after boils down to this:
- Moral absolutism: the presumption that there is a universal, immutable, ideal set of ethics that all people everywhere should try to attain.
- Moral relativism: the presumption that ethics are culturally determined artifacts that can reasonable vary across different eras and different groups.
Relativism and absolutism have somewhat sketchy reputations because the terms are associated with their logical extremes: moral absolutism brings up the specter of fanatical dogmatism; moral relativism, the idea that we might tolerate horrific acts because some other culture believes they are moral. If we ignore those extreme 'straw-man' positions, though, we are left with a subtle and difficult problem. There is a great deal of continuity in moral outlook across individuals and cultures, but also notable — and sometimes glaring — differences. Should we interpret this as the presence of some absolute moral ideal that we all fail to attain in our unique ways (those failures creating observable differences)? Or should we interpret it as mere happenstance, where various cultures have followed parallel evolutions that led them to similar moral codes (that parallel evolution giving a false impression of universality)? There is still a lot of work left to be done in this field.
If you are a moral absolutist, you will not think that your moral ideals apply only to you. You will think your ideals apply to everyone, and (perhaps) that others are failing to live up to them. If you are a moral relativist, then you will assert that everyone else must be a moral relativist as well (even if they claim to be an absolutist). There is a deep philosophical problem of whether we should think in absolutist or relativist terms, but there's not logical problem, because one cannot logically straddle the fence in the way suggested.