I have often heard people talk about, say, "the" twisted $S^2$-bundle over $S^2$. My question is, what do they mean by a twisted bundle? I know that in the above example any $S^2$-bundle over $S^2$ is either $S^2 \times S^2$ or a unique non-trivial $S^2$-bundle over $S^2$. But is that how it is defined? Is a twisted bundle just a non-trivial one, or is it a specific bundle among the non-trivial ones?