Forecast vs Prediction: What is the difference? 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)

Examples:


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.

Examples:


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)
Weather
Sales


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.
Prediction is more general term.
It can be defined as a an expectation for a combination of different predictors (random variables).

Forecasting would be a subset of prediction and mostly related to time-series. Any time you predict into the future it is a forecast. All forecasts are predictions, but not all predictions are forecasts.

Moreover, forecasting always have error, that is why we have confidence interval of 5%, 2.5%, 1% and residuals for modeling. There is no such thing as so called "perfect forecasting", but we can maximize the model accuracy. 

On contrast, prediction sometime can be perfect. I also believe that model should follow data not the other way around.