Looking for help with reading my multimeter.
I would think by moving from 20 to 200, the decimal place would just shift one place. Why when I switch do I get a reading of 20ma vs 10ma?
Is the circuit operating properly in both cases?
Probably the circuit is drawing current in short bursts.
When you have the meter set to the lower current range there is enough drop across the meter to affect the operation of the circuit or i overloads the meter such that it does not average the current correctly.
In those conditions I would put a large capacitor (several hundred or thousands of microfarad) across the supply rails of the circuit to slow down the meter response so it can average the current correctly and the capacitor supplies the current during the pulses.
Typically a DVM has a voltage drop at full scale of 200-500mV so on the 20mA range the meter will have an effective resistance of 10-25Ohms. On the 200mA range it will be 1/10 of that. This extra resistance on the supply rail may affect the circuit.
You're likely affecting the DUT (device under test, the Arduino board) in some way. From the measured current it seems the Arduino is not fully on when it draws 9 mA. 18 mA looks correct. You need to monitor the voltage on the raw pin of Arduino with a second meter while changing ranges on the one that measures current.
Ammeters measure current by measuring the voltage drop across a series resistor. This resistor is small (e.g. 0.1 Ohm) but the value changes depending on the measurement scale. The resistance for the 0-20mA scale will be 10 times larger than for the 0-200mA scale. This is so that the range of voltages generated across the current-sense resistor is the same for all scales.
Having said that, this does not seem to be the issue with the measurement you are making. Perhaps it's something as simple as your multimeter being out of calibration, damaged (e.g., someone sent a large current through it and damaged the current-sense resistor on a specific scale), or of insufficient quality.
I have seen damaged current-sense resistors, despite fused inputs.
In order to not affect the device under test, a high quality meter is required. A meter with an input resistance/impedance of 1 meg-ohm (or higher) is advisable.