The distinction between psychological egoism and ethical egoism reflects the contrast of "is" verses "ought," "fact" verses "value," or "descriptive" verses "prescriptive."
Psychological egoism is the empirical doctrine that the determining motive of every voluntary action is a desire for one's own welfare. On this view, even though all actions are regarded as self-interested actions, the egoist readily points out that people usually try to conceal the determining motives for their actions because such concealment is usually in their self-interest.
Psychological egoism is a descriptive theory resulting from observations from human behavior. As such, it can only be a true empirical theory if there are no exceptions. In science, a purported law only needs one disconfirming instance to disprove it.
Psychological egoism makes no claim as to how one should act. That all persons seek their self-interest on this theory is a purported fact, and this belief is viewed by the psychological egoist as nonmoral and verifiable.
Ethical egoism is the normative or prescriptive doctrine that each individual should seek as an end only that individual's own welfare. The idea here is that an individual's own welfare is the only thing that is ultimately valuable for that individual.
Ethical egoism does not claim that all persons, in fact, seek their own self-interest; ethical egoism only claims that we should or ought seek our self-interest, even though all persons might not do so.
If ethical egoism is to be regarded as a theory, it must be universalized to hold for all persons.
II. By way of clarification of relevant terms, James Rachels, among others, points out common confusion concerning selfishness and self-interest.
Actions in self-interest are not necessarily selfish actions. For example, it is in your self-interest to obey the law, to exercise, and to enroll in college, but no one would claim that it is selfish for you to do so.