Stationarity vs. iid

Hi all,

I came across a statement about iid and stationarity which says that it is unrealistic to assume stock returns to be i.i.d but rather strict stationary. Can someone explain to me what the difference is? Strict stationary means that the returns at time t, t+1, ..., t+n are equally jointly distributed as the returns at time t+j, t+1+j, ..., t+n+j. Correct? The same is true for i.i.d. because one "i" stands for "identical". Also correct? Then I assume the difference lies in the "independence". Are strict stationary processes not independent? Can someone elaborate on this?

Many thanks already