The use of "Big O Notation" itself as a way of referring to algorithmic complexity seems like a misnomer, considering that the topic is about analysis rather than the notation used to express the results of such analysis.
Unfortunately academic textbooks have terrible "UX", so students end up dealing with confusing presentation of topics, hence we're stuck with labels such as "Big O Notation".
Whether I like it or not, by now big o notation has fallen into the category of "folklore" that working engineers use and abuse informally without being very precise about it.
It's like the "proof by engineers induction": if some statement P(n) is true for P(0), P(1) and P(2), then P(n) is true for all n \in Z. :-)
Similarly if an engineer states that algorithm has a runtime of O(f(n)) that should probably be read as "as n grows very large (whatever that means) the runtime approximates (whatever that means) some bound (below, above, whatever) f(n). yolo.".
But people should at least be _aware_ that they are being imprecise about it.
If I read a blog post or StackOverflow post or whatever and I see big-theta notation I know that the person is probably precise with her definition. If I see big-o then it may be correct, or accidentally correct (happens often due to the nature of the definition) or mistaken.
You don't say the best case is O(n^2) if the best case is Theta(n log n) even though technically that would be correct.
/* This is O(scary), but seems quick enough in practice. */