"Time complexity" is a rather vague term and can refer to different things. For instance, there is "worst case time complexity", "best case time complexity" and "average case time complexity". Big O can be used to express an upper bound on any of these. If you don't explicitly state what case Big O expresses an upper bound for, people will assume Big O means "upper bound to the worst case time complexity".
You can also use Big O to express an upper bound to space complexity for a specific case. You can use Big Omega to express a lower bound on either time or space complexity for a specific case.