In both prediction and inference, we estimate a function $f$ that maps the values of predictors $X$ to outcome $Y$. In prediction, our goal is to estimate the function $f$ based on the available values of $X$ and corresponding $Y$ so that we can use $f$ to predict the values of $Y$ for the values of $X$ for which we don't know the corresponding values of $Y$. So, the function $\hat{f}$ can be treated as a black box, and our main objectives are to improve the accuracy and precision of the prediction. In inference, we already know all the corresponding values of $X$ and $Y$, and we're interested in understanding the characteristics of the function $f$ that maps the values of $X$ to their corresponding values of $Y$. So, $\hat{f}$ cannot be treated as a black box and our main objective is to find the exact functional form of $\hat{f}$.