Time Series is a time ordered collection of data points. The observations are taken at a predefined interval of time (may be seconds, minutes, hours, days, weeks etc.). Time series analysis is the study of the ordered data points to extract meaningful insights and its other characteristics.
Forecasting is the science of predicting or estimating for future by analyzing the past and current data. Time series analysis is a very common technique (there are other methods as well) used in forecasting where insights from historical data are used to predict the future data points.
An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Himanshu Singh on 18th January 2019.
Applause for all the respondents- Vastupal, Himanshu, Kirankumar, Manjeet, Prashanth.