example of process s.t. $X_t\sim Y_t$ for all $t$, but $(X_t)$ and $(Y_t)$ has not the same finite dimensional distribution

Question

To prove that two processes $(X_t)$ and $(Y_t)$ has the same distribution, I proved that $X_t\sim Y_t$, but my teacher said that it's not enough, I have to prove that they I the same finite dimensional distribution, i.e. that $(X_{t_1},...,X_{t_n})$ and $(Y_{t_1},...,Y_{t_n})$ has same distribution for all $t_0<...<t_n$. So could you give me an example of processes s.t. $X_t\sim Y_t$ for all $t$, but $(X_t)$ and $(Y_t)$ has not the same finite dimensional distribution ? I can't find any.