1) For one thing, both Sartre's nothingness and my unreality come into the world because of us human beings, who have consciousness and can take various attitudes towards what's going on around us. There wouldn't be nothingness (or unreality) if there were no human (or other conscious) beings, if the world consisted only of rivers and stones, trees and insects. The key to these attitudes seems to be an ability to think of possibilities, of ways the world might be (in contrast to how it actually is, or at least seems to be). "[n]on-being always appears within the limits of a human expectation", and "negation appears on the original basis of a relation of man to the world. The world does not disclose its non-beings to one who has not first posited them as possibilities." (38)
However, compared to unreality (in my sense), these possibilities may remain implied—and will remain so, in fact, in the majority of cases. They form a much more pervasive background in Sartres universe than instances of unreality (which must play out in the world) could produce. Whenever something is missing, absent, or lacking, there's nothingness; Sartre himself brings examples such as the notions of destruction (39–40) and distance (54–55); and eventually lists "absence, change, otherness, repulsion, regret, distraction, etc. [...] which in their inner structure are inhabited by negation" (55). Thus his notion of nothingness is much more inflationary than my unreality, which implies the deliberate creation of what is at least in some respects a 'candidate reality'.
He also has (I think) a much heavier burden of argument to carry for his claim that these négatités, as he calls them, are a feature of objective reality. They're not subjective in the sense that we merely produce them in judgments, i.e. in our descriptions of the world, but there is something in objective reality that precedes them, and is in fact what such judgments are about: "non-being does not come to things by a negative judgment; it is the negative judgment, on the contrary, which is conditioned and supported by non-being." (42) Now, on my account, unreality does come into the world by mere mental activity (thinking, imagining, remembering, and so on), and so it has obviously no claim for belonging to objective reality. Of course, unreality it doesn't come into the world by simple negative judgments, but instead by a rather more complex human activity (for which I've used the broad term 'imagination'). Yet at the same time, the paradigm examples of forms of unreality (the various sorts of fiction, scenarios, lies, dreams, and the future as well as the past) seem to me more specific and concrete in their phenomenology than Sartre's négatités.
2) This may make the scope of these two notions look rather different, and yet there are also some more (and deep) points of agreement.
(Of which there'll be more later.)
 Jean-Paul Sartre, Being and Nothingness. A phenomenological essay on ontology. Translated and with an introduction by Hazel Barnes. NY: Washington Square Press 1992. Quoted with page numbers in the text.
 Where exactly does the line run? Do animals count as conscious beings? In some sense, of course, but I think the way Sartre uses the term it would require more than (most) animals are capable of. At the very least, none of the forms of unreality in my sense are within reach for (most of) them. (I say 'most' because, again, we may have to qualify this a little since latest research seems to find rudimentary forms of self-consciousness in some primates. Some rudimentary forms of unreality, then, might be in play for these as well.)
 A judgment about some instance of nothingness is called a 'negation' in the context from which I'm quoting.