What (I think) I have learned from this thread is that when I use a mutex, then it effectivly acts as some sort of memory barrier as in anything that has been observed by a thread A within or before one critical section where the mutex is locked will also be visible by thread B within or after another critical section where the same mutex has been locked afterwards.
This particularly also affects data that is not stored in the mutex. See also @alice's comment to my other question here.
Atomics, in contrast, will not necessarily ensure that. They may ensure it if you use Release and Acquire (or AcqRel or SeqCst), but that depends on which value has actually been read by the Acquire (i.e. if it was a value written by the Release or any value written by the release sequence).
This is the information that might be helpful for a beginner, I think.
(Not sure if I explained/reflected everything correctly.)