What is the relationship between emission and fluorescence?
You can google all of this for more detail...

Basically an "emission spectrum" is the most general term for detecting photons as a function of energy or wavelength. All the term implies is that your measuring photons. 

A "fluorescence spectrum" is a little more specific. It means that a photon was used to excite the atom/molecule and that the atom/molecule decayed very rapidly with the emission of a photon of longer wavelength (lower energy).