Suppose we have
std::atomic<int> x = 0;
// thread 1
foo();
x.store(1, std::memory_order_relaxed);
// thread 2
assert(x.load(std::memory_order_relaxed) == 1);
bar();
There is, first of all, no guarantee that thread 2 will observe the value 1 (that is, the assert may fire). But even if thread 2 does observe the value 1, while thread 2 is executing bar(), it might not observe side effects generated by foo() in thread 1. And if foo() and bar() access the same non-atomic variables, a data race may occur.
Now suppose we change the example to:
std::atomic<int> x = 0;
// thread 1
foo();
x.store(1, std::memory_order_release);
// thread 2
assert(x.load(std::memory_order_acquire) == 1);
bar();
There is still no guarantee that thread 2 observes the value 1; after all, it could happen that the load occurs before the store. However, in this case, if thread 2 observes the value 1, then the store in thread 1 synchronizes with the load in thread 2. What this means is that everything that's sequenced before the store in thread 1 happens before everything that's sequenced after the load in thread 2. Therefore, bar() will see all the side effects produced by foo() and if they both access the same non-atomic variables, no data race will occur.
So, as you can see, the synchronization properties of operations on x tell you nothing about what happens to x. Instead, synchronization imposes ordering on surrounding operations in the two threads. (Therefore, in the linked example, the result is always 5, and does not depend on the memory ordering; the synchronization properties of the fetch-add operations don't affect the effect of the fetch-add operations themselves.)