quantum mechanics - Schrödinger picture operators that depend on time?

I have been reading up on the Schrödinger picture of quantum mechanics. In this picture it is often said (e.g. here) that the operators are time-independent unless they depend explicitly on time. I cannot see what this is telling us since it seems to be saying that operators are time-independent unless they are not. Is this not exactly the same for the Heisenberg picture which is said to have time-dependent operators? i.e. what does the above saying actually mean and how does it distinguish the time-dependence of operators in the Schrödinger and Heisenberg pictures?