Although non-valid and invalid have the same meaning semantically, I tend to interpret them with a subtle difference.
The difference is the same as that between words like "not useful" and "useless". Calling something "useless" seems to me like a more blatant/harsh way of negating its usefulness than calling something "not useful".
Similarly, I tend to interpret "non-valid" as simply negating the validity of the subject (less intense) and "invalid" as harshly specifying that something is invalid (more intense).
While there would be no book or rule stating this kind of a difference, I believe that our brain inadvertently picks up this kind of cognizance by reading text and observing the minute difference in ways these words are used.
It would be interesting to know if others also feel the same way.
This is an intriguing question. My experience is much like satnam's, only sort of the opposite. The two terms have such similar meanings that dictionaries often use one term to describe the other. There does seem to be a subtle difference in actual usage that I can't find formally documented, and it somewhat relates to a matter of degree. Where our experience differs is that I think of non-valid as the more "intense" term, to use the same adjective. Perhaps it's very situation-specific. Here's my crude attempt to characterize it.
"Invalid" seems to be used to refer to something that is not currently valid or that a reasonable person might mistake for valid, whereas "non-valid" seems to be used to refer to something that under no circumstances could ever be valid. Some examples:
- An invalid license could be an expired license. It was previously valid and could be made valid again via renewal. A non-valid license could be a foreign license that can never be valid.
- An invalid credit card might refer to one that used to be valid but has been cancelled or expired. A non-valid credit card might refer to a credit card that is not one of the brands the merchant accepts.
When a term for validity is applied to an assumption or argument, "invalid" seems to be reserved for incorrect ones a reasonable person might mistakenly make, while "non-valid", if it was used in that context, would cover cases more not valid.
For example, in a serious discussion or debate, one person uses an assumption or argument that seems reasonable on the surface but can be demonstrated to be incorrect. That would typically be referred to as "invalid". Use of "non-valid" would more likely be applied to a more obviously bad assumption or argument where the person making it is expected to know better.
Another example: "Why is John taller than Bob?" "Because Tuesday." People wouldn't be likely to talk about the "validity" of such a response because the argument is so far away from being valid that validity is irrelevant. But I suspect that if someone was to apply "invalid" or "non-valid" to it, the terms would elicit different reactions. "Invalid" would seem so misapplied that people would assume it was sarcasm, even though it is technically true. "Non-valid" would just sound odd, perhaps leading people to wonder if it was some kind of clinical observation rather than off-the-cuff commentary about the content.
So I am also curious to see other responses to the question.