An estimate is a certain measure of a random process which usually applies to the current or previous time period  In contrast, a projection refers to a future time period, and can be considered "an estimate of the future" based on past data. The idea behind making future projections is based on the fact that many real-world random processes are considered to be stationary, meaning that the statistical characteristics (such as mean, variance) of these processes do not change over time. This enables you to use the theoretical distribution based on historical data to predict future events. Note that there are also certain real-world processes that are nonstationary, and using past data generated by those random processes to make future projections can be incorrect. However, in many industries dealing with nonstationary random processes, such as investment, it is assumed that the statistical characteristics of the processes change over time, but not significantly, so the probabilistic approach can still be used to make predictions for a limited future time horizon. For example, if you determine the stock price distribution based on ten years of historical data, it would be safe to use the same distribution for a relatively short future time period such as one month.

In the context of using probability distributions, projections and estimates are performed in the same way, and these terms are used interchangeably throughout the article.