Measuring Audio Signal Similarities
You can use the Normalized Cross Correlation for that.
http://en.wikipedia.org/wiki/Correlation_and_dependence

Basically, representing each recorded sound as a vector, this gives the angle between them. 

Another approach is dealing with features of the sound instead of the signal itself.
You can start by reading how Shazam works:

https://www.google.com/webhp?sourceid=chrome-instant&amp;ion=1&amp;espv=2&amp;ie=UTF-8#q=how%20shazam%20works

http://www.reddit.com/r/askscience/comments/1mdb08/how_do_apps_like_soundhound_and_shazam_work_is/

http://gizmodo.com/5647458/how-shazam-works-to-identify-nearly-every-song-you-throw-at-it

http://www.slate.com/articles/technology/technology/2009/10/that_tune_named.2.html

http://en.wikipedia.org/wiki/SoundHound

http://www.quora.com/How-does-SoundHound-work

http://everythingelsematterstoo.blogspot.co.il/2010/11/how-shazam-works.html