This is fairly obvious but:

Determinism – given a pre-state and a collection of inputs there is at most one post-state and collection of outputs allowed by the system. It rarely makes a good description of what the system is to do. This is a function basically. Non-determinism is more common.

Non-determinism – ‘it’s allowable’ that for some pre-states and collections of inputs, there may be more than one post-state and/or collection of outputs allowed. This is a relation basically. Of course, non-determinism is hard to test because you can run a test multiple times and each time it comes out different.

Examples

Non-determinism allows ‘Don’t care’ conditions, such as:

• “Return either square root”
• “Establish a connection with any printer in the room that can print colour.”
• “Serve any pending requests”

Sometimes, a non-deterministic system is identical (code-wise) to a deterministic system, it’s just different by convention (e.g. instead of specifying an input, ask the system to provide that input as an output).