What is the difference between `compare_exchange` with memory ordering and `compare_exchange` then `fence`

In the document of std::sync::atomic::fence, I see this code:

while self
    .flag
    .compare_exchange_weak(false, true, Ordering::Relaxed, Ordering::Relaxed)
    .is_err()
{}

fence(Ordering::Acquire);

Is it the same with this code below?

while self
    .flag
    .compare_exchange_weak(false, true, Ordering::Acquire, Ordering::Relaxed)
    .is_err()
{}

Or, generally speaking, are these two expressions equivalent in all conditions?

atomic.compare_exchange/*_weak*/(current, new, success, failure)

vs

{
    let result = atomic.compare_exchange/*_weak*/(current, new, Ordering::Relaxed, Ordering::Relaxed);

    fence(if result.is_ok() { success } else { failure });

    result
}

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