correlation-pearson | Pearson product-moment correlation coefficient

Kendall and Spearman correlations are measures of how well correlated two variables are, i.e. how closely related two variables are. The result is a correlation coefficient, which is a statistic that tells you how correlated things are (1 is a perfect relationship, 0 is a perfect absence of a relationship), and in a crude sense, the directionality of that correlation (-1 represents a negative slope). It is also important to note that both Spearman and Kendall correlation coefficients are sensitive to outliers, with the Spearman method being more sensitive.

Robust Linear Regression, on the other hand, is a special case of linear regression, which is a means of finding the relationship between 2 or more variables. You can think of it as a method of finding the "line of best fit". The result of linear regression is the regression coefficients, which is a measure of how (direction and slope) your response changes with your variables.

Often, linear regression uses Ordinary Least Squares, or OLS to find the regression coefficients, with the goal to minimize the sum of squares of your residuals (the square root of the difference between your estimated line and your actual data). This is quite sensitive to outliers: