First of all, O(g(n)) is a set. It is the set of functions f(n) such that there exists positive constants n0 and C, and C*g(n) > f(n) when n > n0.
Second, talking about O(g(n)) does not imply that the time complexity being discussed is the worst-case (or any other case) time complexity. One could for example say that the algorithm A's best-case time complexity is in O(n), and it's worst-case time complexity is in O(n^2).
Second, talking about O(g(n)) does not imply that the time complexity being discussed is the worst-case (or any other case) time complexity. One could for example say that the algorithm A's best-case time complexity is in O(n), and it's worst-case time complexity is in O(n^2).