The RMS calculation for AC power (sine waves) was invented precisely because it is power equivalent to straight, steady DC at that same voltage.
In this way the Tesla/Westinghouse scheme could be directly compared to Edison's DC current -- which is mathematically simpler to understand.
The FULL sine wave is used.
If your meters are accurate, then your circuit build has spurious resistance/ reactance.
You did not build the classic 'low pass band filter' -- ie you did not include a capacitor to buffer the pulses of DC. They may well have been in conflict with the DC ammeter. That is: it couldn't swing fast enough to capture the impressed signal before the signal faded. (It's pulsing at 120HZ, BTW) I'm assuming that the DC ammeter is using a magnetic coil in its pick-up.
(Alert: inductive element thrown into circuit, more than enough to explain such a lightly loaded circuit.)
Your DC reading (4A) is off.
The DC equivalent in amps is 4.5 vs 4.5 -- it's definitional.
(6.36 x .636) I have no idea where that calculation came from. The RMS of a DC steady state circuit has to be 1.000)
A fluttering DC wave form has no obvious, direct mathematical calculation. One merely tests for it. Normally, a capacitor is used to make it stop fluttering. That's what a 'low pass band filter' achieves.