The English language pretty much allows for "modern" and "contemporary" to be swapped at will. Modern Art: Art from the Impressionists (say, around 1880) up until the 1960's or 70's. Contemporary Art: Art from the 1960's or 70's up until this very minute.
Modern art includes artistic works produced during the period extending roughly from the 1860s to the 1970s, and denotes the style and philosophy of the art produced during that era. The term is usually associated with art in which the traditions of the past have been thrown aside in a spirit of experimentation. Modern artists experimented with new ways of seeing and with fresh ideas about the nature of materials and functions of art. A tendency away from the narrative, which was characteristic for the traditional arts, toward abstraction is characteristic of much modern art. More recent artistic production is often called Contemporary art or Postmodern art.
Modern architecture arose out of the rejection of revivals, classicism, eclecticism, and indeed all adaptations of past styles to the building types of industrializing late 19th- and 20th-century society. It also arose out of efforts to create architectural forms and styles that would utilize and reflect the newly available building technologies of structural iron and steel, reinforced concrete, and glass. Until the spread of postmodernism, modern architecture also implied the rejection of the applied ornament and decoration