In my basic definition of a system, I spoke rather vaguely of rules that define how the elements of a system change over time. The example I gave was of Conway’s Game of Life, which contains a set of four rather simple rules. The rules in Life are all deterministic, that is to say that they define exactly what is to happen in a given scenario, but not all rules in all systems are like that.
Some systems may contain random, or probabilistic rules. A trivial example of this might be the rule (for some moving thing) “Go either left or right at random, with equal probability”. In this scenario, the rule does not define exactly what will happen; the thing may go left or right. Importantly, two instances of this system that start in the same state may turn out entirely differently (since one could go left while the other goes right) which is not possible in a deterministic system.
As such, a system is deterministic if and only if all of its rules are deterministic. A single probabilistic rule is enough to make the entire system behave probabilistically, even if all of the other rules are deterministic.
Interesting tangent: There is some debate in philosophy about whether the universe is truly deterministic or random, and while quantum physics is currently leaning in the direction of random that is not (yet) relevant to these definitions.