Differences between linear/nonlinear vs. deterministic/nondeterministic neural nets
Non linear means that there may be a correlation with the input, but it is not a linear one. A function is say to be linear in some argument (the input) when the ratio result/argument is constant. In your case, it is the ratio output/input. Actually, the mathematical definition is a bit more general.

Non determinism is of a different nature. The input/output relation is said to be non-deterministic when one of several result may occur, without any a priori known cause. This is usually modelelled mathematically, either by using a relation rather than a function, of by considering a function from the input domain to the domain of subsets of the output domain.

For example: if you consider inputs and outputs in the domain of integer, for each integer input, you have a set of possible outputs that are all integers.

When this set always contains only a single element, the function is deterministic, and the set can be replaced by this unique element.