I'm supposed to be giving a presentation in an hour involving the differences between analog and digital recording. Originally, I thought that this would be fun because I'm genuinely interested in the topic. But the more I learned, the more confusing it became. Also, I'm entirely unprepared for my presentation.
Up front, the differences are plain. Analog recordings, usually committed to magnetic tape, contain actual waves on them that are ANALOGUES of actual compressions in the air, which we hear as sound. Analog sounds, such as real sounds, are continuous frequencies through time. This means their graph will have a smooth curve over time. Digital recordings capture sound and convert the frequencies into numbers, called samples. Because no more than one number can be assigned at any given moment in time, the graph of the wave is not smooth, but boxy. See the graphs below.
Audiophiles argue that this makes a dramatic differences in how the sound is reproduced and is inferior to analog. A common CD, however, contains 44,100 samples every second. If we think of these samples as film, which is a collection of still pictures moving so quickly that the images themselves appear to be moving, we can begin to understand that a rapid rate of sampling would be heard just as well as an analog recording.
There are plenty of factors that serve to determine the quality of recordings such as sample rate, quality of equipment used to record and the quality of the equipment used for playback. So it's no easy task to definitively say which is better or higher quality or anything. They are two different processes that produce similar results. It is up to the user to determine which method they prefer to use for their purposes.