The difference between those two products is that one includes an analog to digital converter and a digital output, in addition to the analog outputs. You might want the digital output if you have a mac (most modern macs have digital input) but no outboard audio interface. Or if you have other gear with S/PDIF digital input.
Don't trust me (really). Check out the owners manual on the artpro website. There is a signal flow diagram on page 2 that shows you exactly where the A/D conversion occurs. Compare with the analog-only version.
An analog to digital converter measures the voltage of an input signal at a fixed frequency, and converts the voltage to a binary value. Modern ADCs typically support at least 16 bits of resolution at a 44.1 KHz sample rate (CD quality), many support 24 bits at 96 KHz.
It is typical for digital effects boxes to have Analog to Digital Converters (ADC) on the inputs, digital processing in the middle, and Digital to Analog Converters (DAC) on the output. This is because the effects are operating in the digital domain. Preamps are generally analog devices, so any conversion to digital would typically be saved for the output side. You want to do your amplification in the analog domain.