Modern dance emerged in the early twentieth century as a response to classical ballet. Pioneers developed named techniques (for example Graham and Cunningham) that emphasized personal expression, grounded movement, and often barefoot work rather than ballet’s fixed positions and stories.
Contemporary dance grew out of modern dance around the mid-twentieth century. It is not tied to one fixed technique: choreographers combine modern and ballet with theatre, visual art, improvisation, and influences such as martial arts or street forms, so each work can invent its own movement language.
In short, modern dance has historical techniques and styles rooted in that revolt against ballet; contemporary dance builds on modern and ballet but stays more open and continually evolving. Source: Nederlands Dans Theater — Modern dance or contemporary dance?