The noun "sax" can refer to the entire saxaphonefamily of not-so-musical instruments, and generally refers to the most common "sax", that being the alto saxaphone. It was abbriviated in order to not be so long as to confuse the already-addled minds of those who actually enjoy playing the instrument.
"If you honk that sax one more time, I'ma gonna take it and throw it in the bay!"