Most DVMs have a constant input impedance of 10 M ohms on their switched ranges with a higher value for the "plug in" different high voltage ranges.
Analogue meters are basically a current meter with resistors in series to convert them to a volt meter. A good meter might use a 50 micro amp meter giving 20,000 ohms per volt. An old fashioned meter might use a 1mA meter giving 1000 ohms per volt.
If you have a voltage divider of say two 100K resistors across a 5 V supply, their centre point should be 2.5V. Using the 1000 oms per volt meter on its 5V range you would read about 5000/100,000 X 5V = .25 V, using the 20,000 ohms per volt meter on its 5V range, you would get 2.37V, with the DVM you would get2.5V.
Frank