By definition, an “oxymoron” is a combination of contradictory or incongruous words, as in “open secret” and “exact estimate,” while a “paradox” is a statement that’s seemingly contradictory or opposed to common sense and yet is perhaps true, as in “To obey this rule, you’d have to ignore it” and “I can resist anything but temptation.”
In the sentence you presented, “It’s as though there’s an unfinished ending to what could have been a great story,” it looks like the phrase “unfinished ending” may either be oxymoronic or paradoxical. I don’t think it qualifies as either, though. In the context of that sentence, there’s really no contradiction or incongruity between the words “unfinished” and “ending”; the storyteller might have deliberately decided to let the story hang without a formal ending, or might have died before he could supply its ending, so the unfinished narrative or hanging last chapter would be a natural outcome and not at all oxymoronic. There’s also no paradox either in the phrase “unfinished ending,” for there’s nothing in it that seems opposed to common sense yet is probably true; the unfinished ending referred to is, in fact, simply a plain conjecture on the part of the writer and there’s really nothing paradoxical about it.
