Forecast and prediction are actually the same - to tell what is likely to happen in the future based on information available. It depends on the accuracy of the information in hand and the ability of the forecaster/predictor to draw a conclusion after his analysis. For example, weather forecast is based on correlated meteorological observations analyzed by trained professionals to arrive at a logical conclusion.
Divination is the process of a diviner (someone who possesses or claims to possess supernatural abilities) communicating with a spiritual realm to see a picture based on which he can tell what he expects to see in the future. There are countless ways of performing divination. Some of the ways are not methodical. Some others have been formulated to employ a logical system to get a picture by an interpretation of the picture to tell a probable future event based on other known factors affecting the outcome.
The ability to divine depends on (1) the knowledge, (2) the understanding, (3) the last and perhaps the most important, inspiration of the diviner. Inspiration is the reception of messages from the supernatural world. If one does not believe in the existence of a supernatural world, then he is not qualified to be a diviner. Divination should be equivalent to "bullshit" in his dictionary. He should avoid this word to come from his mouth.
There are many classes of diviners. The lowest class consists of people who robotically get a chart from a software and then copy from a textbook all the implications in the chart. If you attend a short (probably very expensive) course and then comfort yourself with the certificate signed by a "Master", then you belong to this class.