I use the two terms as follows:
A prediction model gets features (which can be a time series) as input and gives a fixed-length output (might be multiple values, but "atomic" in some sense)
- Dog vs Cat
- Spam vs No Spam
- Weather for tomorrow
- Sales of next month
A forecasting model gets a time series as input and outputs a single time series.
- Amount of airline passengers: You can predict the value for the next month, but a forecast can be over an arbitrary time frame (with deteriating quality, of course)
I've never seen textbook definitions of those terms. Do you know any source that compares the two terms?
Bonus points if you give me a good German translation for both terms. By now, I call both "Vorhersage" - I have the impression there is no other German word for it.