Some confusion exists because of the way we use words like DAC.
DAC - Digital to analog converter.
In reality - a DAC chipset, a USB, toslink, or spdif chipset, a power supply, an analog output stage.
DAC chipset - The system on a chip which does all of the decoding of a digital stream and conversion to an analog stream. This includes DAC logic, buffers, filters, and in some cases amplifiers. Most DAC chipsets accept an incoming 24bit 192khz stream and convert it into 2 channels of L/R audio. Inexpensive DAC support multiple bit and sampling rates, by reconverting the signal back to 24/192 before rendering it as an analog output. This results in dithering artifacts and an increase in noise which is usually filtered internally (oversampling) before being output as the analog signal. Higher end DAC chips are able to multiclock and so the chip changes it's clock signal for different sampling rates, ridding it of any dithering artifacts and a more accurate representation of the digital waveform. Because having multiple stable clocks is absolutely necessary to prevent jitter, these DAC's can be very expensive. In the pro-audio world this can be somewhat alleviated with interfaces where the clock/sync signal is sent along with the bitstream, allowing bit perfect playback, but in the consumer world including audiophile, this is seldom seen and so most DAC's are self clocked. Individual chipsets have different specifications for SNR, noise floor, dynamic range, operating voltage, and supported digital stream types. Most modern DAC chipsets are built around DVD, blu-ray, and other formats with the exception of DSD DAC's which are used in SACD applications and work very differently than a normal DAC. That's a whole other story though.
USB, toslink, or spdif chipset - These handle the digital input and recreate the digital stream to feed into the DAC. They have little to no affect on audio quality but can have a big impact on compatibility. Whether your USB DAC requires specialized drivers or not, whether it supports WASAPI push or event mode, synchronous USB or asynchronous, and whether the toslink or spdif support high sampling rates, all depends on these chipsets. For recording studio use it's preferable to have chipsets that support ASIO and have low latency operation. For audiophile use this is less important. Poor USB interfaces may also cause clicks and pops due to USB communication issues.
Power supply - Whether it's using a DC to DC converter to power off of USB, or using a wallwart the power supply and how isolated it is from the rest of the DAC can affect things like computer noise, ground loop hum, etc. In general it doesn't matter whether the device runs on plug in power, or USB, so long as the power supply is isolated from the rest of the circuit, is stable, and doesn't introduce noise.
The analog stage - This is where the very low level output of the DAC chipset gets amplified to XLR, RCA, or other line level output. The analog input is amplified and a low pass filter may be used to further reject high frequency noise from the DAC. The analog output stage can sweeten a sound, stifle it, or be neutral. When people talk about a DAC sounding good or bad, it is usually this stage that is responsible for that. You can have the greatest DAC chipset money can buy but if the analog stage kills the dynamic range, rolls off the highs and lows, and changes the phase of the two signals, it's going to sound like rubbish.