Another important difference is that for deterministic chaos you have a simple law that will produce all the values in the attractor. Instead for randomness there is no known recipe to produce past and future values.
We can say the same thing in other ways : for deterministic chaos we can compress all the values in a simple formula, for randomness the only way to represent them is to list all of them.
The formula is the same which is used to generate random numbers on a computer. You can look at a tutorial here.
Almost any iteration can become a random number generator. Now what is the problem:let's suppose that you have the formula and you want to know the value #1000. The only way is to compute value 1, 2 3 ... So the formula is no help for predicting but can become a way to store many,many numbers in a compact way.This is the method of fractal compression.