Luminescence is the emission of light from any substance, and occurs from electronically excited states. Luminescence is formally divided into two categories—fluorescence and phosphorescence—depending on the nature of the excited state.

Both are emission Spectra like you mention. one major difference between the two is fluoscence is observe in solution state while the solid state fluorescence Spectra is known as photoluminescence.

Mr Khan

fluorescence is also observed in solids and gases

phosphorescence is also luminescence as mentioned in the first response

Luminescence is a special case of light emission, so called "cold light". A sufficiently hot object also emits light (continuous spectrum black body radiation), but its emission spectrum is definitely not luminescence spectrum.

Aleksander Balter is right. Emission is a very general term for the insurgence of light. Luminescence excludes black body radiation, but is also another general term for the emission of light, which can be thermoluminescence, photoluminescence, electroluminescence, and so on, depending on the exciting factor, heath (and radiation), light, electrical current, respectively, and so on.

Harry ten Brink thank for correcting me

Actually, I did not read the question properly.