I try to do my best:
First of all, as far as the mathematic goes, upsampling and
oversampling is exactly 100% the same according to digital filter technology (sampling is basically having an electrical signal pass through a digital filter). Upsampling and oversampling BOTH convert a 16bits/44k original signal from a CD into a higher frequency, usually multiple of this 44Khz frequency. I won't go into detail but converting a digital signal into an audio signal (hence the name DAC) can be done much better when the digital signal is at a much higher frequency than the audio signal. Some DAC converts the original digital signal from 44k to 256Khz or even higher before converting to analog signal... So you can say that most DAC have some kind of upsampling done within it, but by convention in the audio industry, any upsampling done inside a DAC is called oversampling.
Pretty much all CD players have some kind of oversampling and this oversampling is all done in one single all purpose DAC chip , especially budget cd player. You can think of a cd player as the below diagram:
Original signal from disk -> oversampling DAC -> preamp
Now enters the Upsampling thing.
You might ask if upsampling as oversampling is mathematically the same then why the fuss?
Physically, an upsampling is a dedicate digital filter that is used solely for the purpose of converting a digital signal to a higher frequency that is multiple of the original signal (as opposed to a DAC which has to upsample the signal then have to convert the signal to analog). This "upsampling signal", after passing through the upsampler, then get inputed to a DAC then the DAC would upsample some more, perhaps to 256K, then coverts it into analog. With upsampling the above diagram can be view as followed:
Original CD signal -> upsampling to 96 or 192 -> ovesampling DAC -> preamp.
The trick is you have to use a high quality dedicated digital filter for your upsampling stage. If your upsampling is crap, then everything else after that will be crap so you would be better off without all this upsampling altogether. In most cases, it's a lot easier to make a high quality upsampler by itself than to having to incoporate it into a DAC. Of course, you can make a very good, high quality stand alone DAC and can outperform a so-called CDP that uses upsampling technology, but I guess that it is more cost-effective to use upsampling as opposed to spend all that money into a really complex, high quality DAC.
Hope this help.