Let us imagine a simple case. We have three tiny people, each of whom is placed in a box with a pencil and a limitless supply of slips of paper. Every minute, they each write a number on a slip of paper, and slide it out through a slot in their box.
One of these people has "free will". By this we mean that the person can choose to write any number he or she feels like.
Another of these people has a book of predetermined numbers in the box, and is instructed to copy these numbers onto the slips of paper in sequence.
The third person has a source of entropy-- let us say a lava lamp-- and copies numbers based upon a suitable formula applied to an element of the entropic source.
Given this scenario, a few things become evident.
First of all: there is no way-- and I mean absolutely no way-- that we can rigorously determine which of the three boxes contains which of the three people based upon the numbers output. We don't know which of the number streams is the product of free will, which is the product of a determined process, and which is the product of chance.
Second: upon closer examination, we see that each of the three alternatives is actually problematic, even if we know which person is in which box. The predetermined list is following a deterministic process in that it is copying numbers from a book, but we don't know where the numbers in the book came from in the first place. Were they freely chosen, randomly chosen, or determined according to some other process? We can't tell (due to #1 above). Similarly, the allegedly random numbers are coming from a source of entropy (such as a lava lamp), but how can we tell if this is truly random, or if it is determinate? Can we be absolutely certain that there is no physico-mathematical model that will accurately predict the movement of the fluid? Finally, the alleged "free choice" was made by a person according to what he or she "feels like" choosing, but where do these feelings come from? Can we be certain that there is not a deterministic process that is controlling the brain chemistry and synapse-firing to cause certain numbers to be chosen?
So, where are we, then?
We are left with the sad fact that we have no means by which to provide a rigorous definition for any of the terms involved, and must rely purely on our intuitive sense of what they mean in context.
Fortunately, this is not really a problem, since the so-called problem of free will isn't really much of a problem, anyway. It certainly appears to us that we have free will, and our actions are predicated on that belief. If that belief is erroneous, precisely nothing changes in our actions-- it cannot, because if the belief is erroneous and our actions are determined, well, then they are determined and are what they would have been. So, at the end of the day, it is much ado about nothing.