The problem is the nature of a "rectified load". It isn't anything about the "digital nature", that would be more of an issue on the output if it were an issue anywhere.
But, especially at low currents, the rectifier pulls current in short pulses. Those short pulses are mostly made up of high frequencies (harmonics), much higher than the 60 Hz The usual analog meter like an "Amprobe" is good for low frequency, because it is intended to measure 60 Hz current, with a few harmonics.
When the current is MOSTLY harmonics, the meter does not respond to most of them, and may read completely wrong. You'd probably get a much closer match between the meter indication and actual if the VFD were powering a heavily loaded motor, because the hevy load will "spread out" the pulses of current so they have much more low frequency content.
Any decent "true rms" meter will read many more harmonics and give a much more true indication.
The meter reads closer on the "digital" output, because the motor inductance forms a filter which eliminates most of the high "digital" harmonics, leaving frequencies that the meter can read.
Reasons:
The rectifier charges up a capacitor in the power supply. The rectifier conducts current only when it has voltage difference across it in the "forward" direction. With NO load, the capacitor charges up to the peak of the line voltage, and then there is no more voltage difference, so current stops flowing.
With just a small power drain from the capacitor, the voltage does not drop much. Therefore there is no "voltage differerence" across the rectifier until the input voltage is very nearly at the maximum peak voltage. When the voltage goes above the capacitor voltage, the rectifier conducts and "refills" the capacitor, at which point current stops again. So there is a very short "pulse" of current, which is mostly rather high harmonics of the 60 hz. Analog meters often do not read those high harmonics well, if at all.
With a hevier load, the capacitor voltage drops farther, so the current pulse starts sooner, and lasts longer. That means the pulse has much more low frequency content, that an analof meter can read.