The SEM (standard error of the mean) quantifies how precisely you know the true mean of the population. It takes into account both the value of the SD and the sample size. Both SD and SEM are in the same units -- the units of the data.
Does standard error of the estimate have units?
The Standard Error of Estimate: How Large are the Prediction Errors? The standard error of estimate, denoted Se here (but often denoted S in computer printouts), tells you approximately how large the prediction errors (residuals) are for your data set, in the same units as Y.
Does standard deviation have units?
The standard deviation has the same unit as the variable, and will scale with them when you change units. The correlation coefficient, on the other hand, is unitless.
