My own (unsystematic) sense of the matter is that divination involves the use of certain tools or techniques to gain insight directly from the spiritual or supersensible realm. Prediction and forecasting necessarily involve current statements about future events. Divination may, but need not, be used as a predictive tool. For example, you may use a tarot spread to get the "lay of the land" spiritually, more of a current snapshot. We also use the verb "divine" to mean ascertaining what is unknown by means other than ordinary cognition. So we may say that someone "divined" what we were thinking.
Also, my own experience with divination is that, used correctly, it possesses a depth and subtlety that other, more mundane predictive devices or techniques lack. For example, if I am offered a new job and consult the tarot, I may ask "will I succeed at it?" And the answer may be no, so I would not take the job. But if I ask "Should I take the job?" or "What will be the outcome if I take the job?", I may get a positive response, even though I will fail at the job, because that failure will teach me something I need to know. Divination is the right tool for that type of insight into the future.