Have the two words randomness and unpredictability the same meaning in mathematics?

Question

Given a random variable $X(t)$, the value of $X(t_k)$ is independent from the vaue of $X(t_{k-1})$ and more, the value of $X(t_k)$ can't be deduced from the previous $X(t_{k-N})$ values. So at the time $t$ the value of $X(t)$ is unpredictable. If I have a process $Y(t)$ in which the value of $Y(t_k)$ is dependent on the previous $Y(t_{k-N})$ values in a very complex way and $N$ is very high, I am unable to forecast the value of $Y(t)$ at time $t_k$, but the precess is deterministic even if I could consider it random. So in my concern randomness and unpredictability doesn't have the same meaning. Could a random process can be considered a deterministic process in which the value of $X(t)$ at time $t_k$ depends on the values of the previous $X(t_{k-N})$ when $N\to\infty$? Thanks.