Different elements emit different emission spectra when they are excited because each type of element has a unique energy level systems. Each element has a different set of emission colors because they have:

Different elements emit different spectra when their electrons get excited because each element has a different arrangement of electrons surrounding the nucleus. The energy levels in which the electrons can occupy are unique to a specific element. When an electron gets excited into a higher energy level, it will eventually relax back into its original state and emit light corresponding to that energy.