as others already said, high CV types of MLCC have a big variety on their nominal capacitance value, especially when you have low grade ceramics, or a no name manufacturer.
High CV means either high voltage and/or high capacitance value for a given size.. look out for "edge" value type, i.e. the highest values in a series.
Every MLCC above 1µV mostly suffers from degradation (decrease) of capacitance versus temperature, time and especially versus applied DC voltage, on the order of many 10%. The manufacturers, especially the bad ones, then tend to deliver much higher initial capacitance values, like +30%.
If you have a 22µF / 6V3 capacitor, and you measures its capacitance at 5V working voltage (typically behind a LDO), you will notice that its capacitance might degrade by -50%, and additionally by e.g. -20% over time, when this operational voltage near its nominal voltage is applied continuosly. This might lead to instabilities of the LDO, because it really needs these 22µF.
If the application is run at automotive grade temperatures, like +85°C, additional degradation sets in. Most of these effects are reversible.
All these effects might lead to the different measurements, depending on the method used, i.e. if the measurement is done on a small DC level, or at high DC levels.
The DE5000 uses practically zero DCV and an AC method, whereas DMMs often use a DCV charging method.
To check your 34461A, you might compare film capacitors, where you don't have these effects, but it's difficult to get them at higher than 4µ7.
Frank