This paper by Anderson, Bollerslev, Diebold and Labys documents an empirical finding about standardized returns.

If one needs to obtain standardized returns, the usual way is to divide the returns by volatility estimated  by ARCH, GARCH type of models. This does not eliminate fat tails though. This paper studies 10 years of high frequency returns for USD-Yen. It begins by showing that the unstandardized returns are fat tailed(obvious to everyone in today’s world). Subsequently the returns are standardized via realized volatility. The analysis shows that returns standardized by realized volatility appears slightly thin-tailed. Subsequently the authors a multivariate standardization of returns and find that  returns standardized by modeling joint behavior of realized volatility, are close to i.i.d.

So, why is there a between the behavior of returns standardized by GARCH and returns standardized by realized volatility ? The difference arises from the time component. GARCH considers data up to time t , but realized volatility calculations consider data including time t. Subtle point, but it makes all the difference in the way standardized returns behave.