What wave spectrum identifies the waves in am and fm?

There's really no big physical difference between AM and FM radio waves.

In the USA, commercial broadcast AM radio stations all operate at frequencies between 550 KHz and 1.7 MHz.  Commercial broadcast FM stations operate at frequencies between 87.9 MHz and 108.1 MHz .

So when it comes to AM and FM transmissions for public "education, information, and entertainment" (and selling stuff), the wavelengths of the AM stations are much longer than the wavelengths of the FM stations.  But this really has nothing to do with them being AM or FM.  It's just the place in the radio spectrum where the US government assigns various types of radio communication services.