In music|lang=en terms the difference between triad and quartet
is that
triad is (music) a chord consisting of a root tone, the tone two degrees higher, and the tone four degrees higher in a given scale while
quartet is (music) the set of four musicians who perform a piece of music together in four parts.
As nouns the difference between triad and quartet
is that
triad is a grouping of three while
quartet is (music) a music composition in four parts, each performed by a single voice or instrument.