Generally speaking:

Classical Composition is rooted in the tradition of western classical music that developed through the baroque, classical, and romantic eras into more contemporary and diverse cultural styles in the 20^th century. Classical composition students study classical theory, counterpoint, orchestration, analysis and keyboard skills. Students in this program generally compose music for live performances for an audience in a recital hall, and music for films.  Score based music notation is central to the Classical Composition method.     

Studio Composition is rooted in the tradition of popular music songwriting and the composition of music for commercial production, recordings, film, media, and pop/rock style concerts. Students in this program generally compose music that is produced and recorded in a studio, sometimes using live musicians, and sometimes using virtual instruments and music production software.

There is some cross-over between the two programs, which is consistent with the intersection of these styles in contemporary musical culture.