OLS stands for Ordinary Least Squares. OLS is a line or estimate which minimizes the error. The sum squared of errors is considered here. Error is the difference between the observed value and its corresponding predicted value. This is typically in a linear regression model scenario. MLE stands for maximum Likelihood Estimate. MLE is an approach for estimating parameters of a statistical model. Here random error is assumed to follow a distribution, e.g. normal distribution. MLE is more to select a parameter that can maximize the likelihood or log-likelihood (when we try to normalize based on data values). OLS considers the parameter value that minimizes the error of the model.