There are several different (sometimes related) mathematical objects called ”spectrum” or whose name has ”spectral” as prefix:
inlcuding spectral theory such spectrum of an operator, spectra of families, of a Banach algebra, Gelfand spectrum, prime (primitive etc.) spectrum of a commutative or noncommutative ring, analytic spectrum, spectrum of an abelian category, Orlov spectrum of a triangulated category etc.
There is also a notion of
which has no particular relation to other notions of spectrum .