Forecast and Prediction though seemingly synonymous, in literature, in analytics conversation they do possess a considerate difference. Most of the times in a casual manner both of these terms forecast and prediction are used quite interchangeably while referring to value estimates in future with certain probability. In reality, they need to be differentiated and as a Data Analyst knowing the difference is an essential part of communication.
Forecast are value estimates for the future based on the study of the historical data. Forecast are time dependent and values are estimated based on observation made on a regular time interval scale.
E.g.: Forecasting, what would be the demand of a product for next three months in a retail store. In this example, in a simplest form, the demand can be estimated based on the past observations of the sales of the product over the months, assuming none of the market conditions have changed the demand is going to follow the same pattern as in the past.
Forecast allows inclusion of time based future knowledge into the estimates. Like accounting for future months market projections, holiday schedule, weather forecast etc.
Time series models such as ARIMA, ARIMAX, Moving Averages, Exponential Smoothing etc. are forecasting models used for weather forecasts, demand forecasts, sales forecasts etc.
Prediction are value estimates, not necessarily for the future, based on the study of a set of events, instances to be precise. Predictions are not time dependent and the values estimated are based on observation made on the provided set of events.
Prediction uses cross-sectional data where observations are considered without regards of time or under a consideration that observations are measured at same point in time, unlike time series data where the observations are time dependent.
E.g.: Predicting how the demand of a product A will get effected when product B prices are increased. In this example the demand can be estimated based on the past observation of the relation between sales of Product A and price of Product B.
Predictions are not necessarily always has to be into future. Like in classification models where if the goal is to classify if an event is fraud or not, the event can be predicted to be fraud or not based on the observations from the past fraud and non fraud events.
Prediction models such as Regression models, classifier models etc. are prediction models used for marketing effectiveness, pricing, fraud detection etc.