Discussing the semantics of the words "forecasting" and "prediction" is drifting dangerously close to being off-topic, so I will only comment on this once.
As with all models, do they ever predict anything?
No. They estimate, they calculate probabilities, they take knowns into account and they are unaware of black swans; and that's it.
Indeed. We aim to get a model that somehow reflects the thing we are modelling, and hence we can interpret the numbers we get out in some useful way. The interpretation and presentation of the output of models can sometimes be as hard as writing the model in the first place.
You can make true claims about the future. And those are the ones that would fall in the category of predictions.
Sorry for being pedantic here, but is my understanding of the word wrong?
The problem isn't that your understanding of the word is wrong: the problem is that there isn't a clear, precise, scientific definition of the words "prediction" and "forecast". It will vary from one discipline to another (and even within the same discipline). And then we've got "normal" day-to-day use of the words. Largely, they are interchangeable in English - although, stylistically, one often works better than the other.
In common parlance, "forecast" sounds more scientific than "prediction": hence we watch "Weather Forecasts" on the news, not "Weather Predictions", and a crystal-ball gazer makes "predictions" about the future (which are mostly wrong), not "forecasts". But... it would be perfectly acceptable to say that "Model X predicts Y": as per "Einstein's General Theory of Relativity predicts a gravitational lens effect of 0.0001 degrees". "Forecast", in this case, would just sound wrong (to me, anyway).
Personally, I don't think there is a lot of point getting hung-up on the use of those words. I'll go with whatever people feel most comfortable with - or I'll just try to avoid using the words and write math(s) instead