Hi,
In a philosophical context, they mean the same. At least as far as I know.
Well, that's not immediately obvious to me. Let's examine these words a little, shall we?
unreality The prefix 'un-' suggests 'not...', 'an absence of..', or 'the reverse of..'.
nonreality The prefix 'non-' suggests 'not ...'.
Consequently, can it not be argued that the two words are not necessarily the same? In particular, if we are thinking of philosophical niceties, surely the absence of reality or the reverse of reality are not exactly the same as the non-existence of reality? Prefixes convey unique distinctions. If you doubt this, consider for example the words interested, uninterested and disinterested.
Now let's consider what is a valid word. In English, we allow ourselves a lot of freedom in adding 'un-' and non-' to words. However, it's not complete freedom. We accept 'a non-prescription drug' but not 'an unprescription drug'. We accept 'unlocked' but not 'non-locked'. 'Unreality' is a word in my dictionary. The word 'nonreality' is not in my dictionary. Google, for what it's worth, shows many more hits for 'unreality'.
Does that mean we should object to the use of 'nonreality'? Perhaps. I might add my personal suggestion that we should object a bit more strongly if philosophers use it, because these guys are already notorious, I would suggest, for taking liberties wth the English language! Ha-ha! Certainly, my belief is that it's better to make your argument by sticking to words in the dictionary. If you don't, I think it's incumbent on you to ensure that your definition of a non-standard word is clear to your audience.
Best wishes, Clive