@Audiophiliac
Here's a comparison between the same song but different sample rates. I took an audio file with a sample rate of 176400Hz. This is the actual sample rate of the recording, it's not upsampled. Keep in mind that the difference between different sample rates are the different cut-off frequency of the analog signals they can represent. So I low-passed this file with a cut-off frequency of ~20kHz. The recording still has the high resolution sample rate, I only removed the high frequencies. After that, I downsampled this file to 44.1kHz.
Here's a comparison between a slice of these file's waveform:
First of all, notice that I'm using music, not some obscure test signal. This is a very, very short slice of the music I used so you can get a better look.
There's something we have to clear up. The bottom image shows the "stairsteps" as the samples are being connected in a very simple way. This line is not what the ADC encodes. As an aside, a signal that looks like the stairstepped line would never come out of an ADC because an ADC usually puts out a PCM signal which looks nothing like that. The point of the PCM signal is not to encode information about the stairstepped signal. The output of the ADC encodes information about the continous signal which looks just like the one overlaid on top of the stairsteps.
Something you might find more interesting is the top picture. It shows what a digital audio signal is in a less misleading way. The samples are not being connected the way they are on the bottom picture. Since a digital audio signal is discrete in time, it's a better representation. Notice how the orange line that the digital audio signal encodes is smooth. Also look at how precisely the peaks are represented. They don't have to coincide with the sample points at all, the timing of the peak does not matter, it gets encoded properly. The orange line also looks exactly like the analog voltage (if you looked with an oscilloscope, obviously noone can "see" voltage) that would come out of the DAC if you fed it the digital audio signal the white dots show.
Lastly, notice how similar the top and bottom pictures are. The similarity might be unexpected to you since the music I used have a sample rate of 176400Hz and the top picture shows the 44100 signal. The reason they are this similar is because the 176400 sample is low-passed as stated before. Since it is low-passed, a digital signal with a sample rate of 44100Hz can encode it just as well as a digital signal with a sample rate of 176400Hz. The extra sample points included in the 176kHz file have no use, as the extra sample points added during the recording don't carry any extra information about the band-limited analog signal it represents.
I could also send you the tested songs so you can compare them (test if they not only look the same but also sound the same) yourself by a
properly conducted blind test.
Also the last couple pages of the discussion would fit better an some other threads, including this post I guess.