In following Konstantinos, compassion is literally a "suffering with" somebody else or with the "other" in terms of an immediate and existential situation or context, or because of a past experience that allows one to "suffer with" another. Pity comes from a position of superiority or authority over the other, whether real or imagined. So, Hengki, I agree with you that they are not the same. If I am compassionate it is because I do not pity another.
Dear Hengki, I would concur with Nicholas regarding pity developing from a position of authority and superiority. I work in the field of mental health nursing and regard myself as compassionate but have never (knowingly) demonstrated pity, for the very reasons mentioned. Your question also bears resemblance to similar debates concerning empathy and sympathy - sympathy like pity may be a reaction to a person or situation where empathy and compassion can be developed and used in a more productive and helpful manner in my opinion.
I think that all the previous answers point to crucial differences between compassion and pity. As I see it, compassion can be equated to empathy and it involves two components: (1) a cognitive component; and (2) an affective or emotional component. In other words, when compassion or empathy is the case we should be able, first, to identify what another is feeling or experiencing (e.g., feeling good or happy, or feeling bad and unhappy) -- the cognitive component of empathy -- and, second, to share another's feeling, the affective component of empathy or compassion. Literally, pity means to feel sorry for another's situation without necessarily sharing his/her emotional or affective state. So, compassion and pity are two different reactions to another's physical or psychological situation. The former has a positive tone that does not exist in the latter. To have pity of another reminds me of patronizing and a vertical relation. Compassion and empathy remind me of a horizontal relation. If a were in a bad situation, I would like to have nearby compassionate people, not people that feel sorry for my bad situation. Literally, sympathy means suffering with somebody else. As I see it, in contrast to empthy, sympathy does not involve a cognitive component for it is, say, a visceral reaction. There is accumlated evidence that shows that babies are capable of sympathy, for example, to cry when another baby is crying, but not of empathy. All that said, it should be mentioned that there is a huge literature about the differences between compassion and pity, and empathy and sympathy. This literature points more to controversy than consensus, which is no surprise to me because psychological concepts are, in contrast, for example, to physical concepts, elusive concepts.