Contemporary dance emerged in the 1950s as the dance form that is combining the modern dance elements and the classical ballet elements. It can also use elements from non-western dance cultures, such as African dancing with bent knees as a characteristic trait, and Butoh, Japanese contemporary dancing that developed in the 1950s.
Commercial dance would encompass a myriad of styles. Mainly in the form of Street Jazz, which you see in music videos. It can also be what you see in cruise ships shows and Vegas type shows too. However, because dancers who are commercial dancers are trained in many styles of dance, it can be narrowed down to what you see in music videos. That is a street jazz and a combination of hip hop and modern jazz.