Chaotic systems are deterministic (as shown by a deterministic computer algorithm simulating one). They just aren't predictable except by simulating them (which constrains us by time and accuracy).

No, that's not it.

Chaotic systems are very sensitive to input conditions, where a tiny change yields a completely different result.

With a non chaotic system a small change in the input yields are small change in the output, so it's possible to calculate approximately and get useful results, not so with Chaotic systems.

I don't think that conflicts with what I said?

I don't think it conflicts with it, but I believe the correct explanation has to do more with tiny changes producing big ramifications than with being deterministic or not.

That's why the "butterfly effect" is used as an explanation of chaotic systems (albeit in my opinion a not a very good one).

Edit: changed contradict to conflict

For me, the most interesting part of Chaos is that it is deterministic.

Meh, it's mathematically deterministic. In reality there is always error (modelling error, measurement error, simulation error) which means that chaotic systems are effectively random on long time scales, even though they are technically deterministic.

I would disagree with the phrase "effectively random" because its too general. Chaotic attractors survive the presence of noise and Chaotic systems look nothing like random data when viewed in a certain way.

Another way of looking at real systems, is that the system is deterministic and the errors are random.

I've checked that (source is a text written by physicist Hans-Peter Dürr, who worked with Werner Heisenberg in the past), a real double or triple pendulum is from time to time chaotic and uncalculable (if started with strong impulse).