The most general feeling of sorrow or unhappiness can be captured with the adjective sad. The word bitter, on the other hand, describes a more pointed feeling, often one of disappointment, sharpened by resentment, hostility, or cynicism. A bitter sorrow is one that is deeply grievous or hard to bear. A bitter lesson is one that is hard to accept. And bitter rivals are competitors whose relationship is marked by intense antagonism or hostility. In all of these, you can find traces of bitter's earliest sense in English: "having a harsh or disagreeable taste."
To be jubilant is to show great joy or triumph. Contrasted with the word happy, which conveys delight but not necessarily to a high (or noisy) degree, jubilant shouts its elation from the rooftops. It comes from the Latin verb jūbilāre meaning "to shout, whoop," and fittingly, you're most likely to find it describing the mood or manner of people gathered in celebration, or with something to "whoop" about, as a success or victory.
Usually when we use the word different, we are describing something that is unlike something else. The word disparate conveys that, too, but the distinction is more pronounced. Items, attitudes, or systems that are disparate are so dissimilar or incongruous that they are difficult to compare, and may indeed seem incompatible. Despite this word's prickly disposition, disparate is often found in discussions of efforts to bring things together or find common ground.