"Not possible" and "Impossible"
When we say,
It is not fair.
or
It is unfair.
I'm not sure enough to say whether both of the sentences have the same meaning or not though superficially, there is no difference between them but if we say,
Something is not possible.
or
Something is impossible.
then there is really an observable difference in my first language. Hence, the question - is there a difference between the preceding two sentences in English?
Solution 1:
To me the only difference is style: one word (unfair) versus two words (not fair). The same for impossible and not possible: both mean cannot be done for some reason or other.
Solution 2:
I don't think there's any difference of meaning between unfair and not fair, or impossible and not possible; but there are all sorts of other reasons why you might choose one over the other. A few examples:
Discourse Context — If someone says to you, “This proposition is not very probable”, you would very likely mirror his construction and say “Not probable? It's not possible!” But if he had said “This proposition is improbable” you would respond "“Improbable? It's impossible!”
Register & Rhetoric — If you have seen the movie The Princess Bride you may recall that Vizzini is given to saying “Inconceivable!”, and is eventually rebuked by Fezzik that “I do not think it means what you think it means.” Vizzini's use, of course, is ordinary colloquial hyperbole, and “Impossible!” is often used the same way. Accordingly, in conversation, when you mean impossible literally you may prefer to say not possible, so that you will not be understood to mean merely very unlikely.
Prosodic Context — The im- in impossible and un- in unfair are unstressed syllables, and don't take stress as readily as not. Small children (in my experience) always shriek “It's not fair!” rather than “It's unfair!” when someone else gets something they want—somehow the spondee is just more indignant than the iamb. In print, similarly, you might use not possible if you feel that italicizing the first syllable of impossible (impossible) doesn't emphasize the negative adequately—or if, like me, you've never figured out how to emphasize just a segment of a string in these postings.