Since modern, scientific psychology was originally (though debatably) inspired by classical psychoanalysis, people tend to get the two confused. Even with the radical differences between the two, one still often sees the word "psychology" used in the same writing as terms like "penis envy" and "Oedipus complex." This is a dangerous dilution of science in that it appeals to everybody's wish to understand themselves, uses ideas and relationships that can be easily understood by the layman, and is also completely unfounded and incorrect. When put together with a willing populace these ideas lead to heaps of supposedly educated people who believe they have deep insight into their peers, friends, and culture, but who are actually profoundly wrong. In the process psychology -- the real science with the correct explanations -- is ignored and layed to the wayside.

Here's the difference:

Psychoanalysis: The use of circular reasoning (the patient's description doesn't fit my diagnosis, so he must be in denial, etc.) to try and show how hundred year old unfounded findings are fact. Freud and the rest inferred their findings from individual case studies, and set up the system in such a way that any conflicting data could be thrown out as denial or repression. This approach is the exact opposite of real science, where controlled experiments are done on large groups of subjects, and when the data don't match a given theory, that theory is modified or discarded. Psychoanalysis is pseudo-science at its most ugly, because (unlike UFOs and Bigfoot) an enormous and unfortunate deal of attention has been paid to it by Western culture.

Psychology: The use of modern, experimental and comparative methods to determine how the human mind functions, and how that function relates to our behavior. Psychology uses data that can be measured and compared to one another as evidence for theories that may be proven or disproven at some point in the future. Science, pure and simple. Perhaps not as "hard" as physics or chemistry where all stages of the process are observable, but science none the less.

In the words of a psych professor I once had: Freud was wrong. Freud is dead. That is all.