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No, that’s all correct.
The key concept is "Input impedance" (of the multimeter), and generally speaking, you want the highest possible impedance. Cheap analog meters tend to have lower input impedances – in the few thousands (5K – 20K) of ohms, though the higher-end analog products like the Simpson 260 have far better specs. Digital meters, on the other hand, tend to have much higher impedance – in the range of one million ohms (1M) on the low end, and 10M – 11M on the upper. Even the cheap digital meters have a far higher impedance than any** analog design.
In short, the higher the impedance, the less burden the meter places on the measured circuit. As impedance falls and burden increases, readings become more skewed.
(** We’re excluding VTVMs and FETvoms, etc.)