Quant: SEE and RMSE specific, specified, different, why

strikethree

Since
SEE = MSE^0.50
And
RMSE = MSE^0.50
Mathmetically, SEE = RMSE, but why are they named differently? In time series, RMSE is used to compare different AR models to see which ones are best specified for predicting out-of-sample forecasts. Is SEE specific to in-sample forecasts?

mfleming1983

SEE: in-sample.
RMSE: out-of-sample.
In either case, the smaller the value, the better the model.