As Alan said, the hardware DVM will have significantly lower bandwidth than the scope, so that's a possible source of error.
Another source would be the fact that you're averaging a noisy signal. which inherently changes your measurement as the noise is part of your signal and counts to RMS too.
I also see some very fast spikes on your averaged waveform, which could be an artifact of trigger jitter+averaging which will affect your measurements.
The DVM measurement is done through hardware similar to digital DMM. It's inherently much lower bandwidth than the scope channel.
It also runs independently of the acquisition hardware, it's a live read of what's on the channel at that moment, not what was on it during the last acquisition.
The other measurements are calculated after the signal is captured by the ADC and processed (for your example, in your case, the waveforms are averaged before measurements are taken) and are calculated again when a new acquisition is displayed.
So there are, at least, 3 ways in which the measurement and DVM systems work that could explain the discrepancies you're seeing: bandwidth, post-processing and triggered/free run.