If you mean "same song" in the iTunes sense of "same recording", it would be possible to compares two audio files, but not by byte-by-byte comparison of an encoded file since even for the same format there are variables such as data rate and compression that are selected at time of encoding.
Also each encoding of the same recording may include different lead-in/lead-out timings, different amplitude and equalisation, and may have come from differing original sources (vinyl, CD, original master etc.). So you need a comparison method that takes all these variables into account, and even then you will end up with a 'likelihood' of a match rather than a definitive match.
If you genuinely mean "same song", i.e. any recording by any artist of the same composition and lyrics, then you are unlikely to get a high statistical correlation in most cases since pitch, tempo, range, instrumental arrangement will be very different.
In the "same recording" scenario, relatively simple signal processing and statistical techniques could be applied, in the "same song" scenario, AI techniques would need to be deployed, and even then the results I suspect would be poor.