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DAC - abbreviation of “Digital (to) Analog Converter” turns digital signals into analog ones. In the context of hifi, a DAC is usually a box with some inputs like USB, SPDIF, TOSLINK, AES, etc. and outputs in the shape of RCA, TS/TRS or XLR.
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Amp - Amplifier. Turns “line level” analog signal into “speaker level” signal. There are various Amplifier Classes.
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Audio Interface - Combines a DAC and an ADC (= Analog (to) Digital Converter) into one unit. This way you can record sound to the digital domain and turn digital signals into analog ones.
A lot of Audio Interfaces include pre-amps and phantom-power options.
I could see that, yes. The Big-Knob series is really meant for this “on desk, direct control”-use case you have.
Same target use as the BigKnob, just less functions to keep the user interface simple.
Main concern over the BigKnob would be accidentally switching on Phantom Power.
Between the two, I would take the BigKnob Studio because it gives you the dials to set up headphone and monitor levels independantly (I think, would have to check the manual).
The Audient iD22 “fixes” that shortcomming, at a price.
Edit: Just to note this again. The Shure SM7B needs a good pre-amp.
Other options on that route would be the Yamaha AG-03, Solid Stage Logic SSL2+ or Fluid SRI-2, not sure how well they would do driving your headphones.