How can I tell if something's controlled by an analog or digital input?
Like you already suspect a DMM won't give you necessarily the answer. If the only levels you read are only 3.3V (capital "V", since it's derived from a person's name) and 0V it's a safe bet that it's digital. A PWM signal is also digital, but will show a voltage between 3.3V and 0V on a DMM, since it includes a low-pass filter. The DMM won't tell an analog and PWM signal apart. You'll need an oscilloscope to actually see what the signal looks like.  

If you can trace the signal back to the output of a microcontroller, without filtering, it's most likely a digital signal. While most microcontroller families are available with on-chip ADC, very few also have DACs on board.