Just like events in history, every piece of art was created during a certain period. Each period of art had specific styles and influences. The styles of art have changed through the periods. Many artists through art history were grouped and were called an art movement as they all shared a similar style during the same period.
Any art created after the 1950's up today was created during the Contemporary Art period. Contemporary Art can be anything from a painted photograph (Photorealism) or a piece of graffiti, and so much more. Pop Art, Young British Artists and Op Art have been movements during the period of Contemporary Art.
The period of art before the 1950's, from 1850 to the 1940s was known as Modern Art. Art movements during this period were: Impressionism, Surrealism and Post Impressionism to name a few.
Van Gogh- Modern Art Post Impressionist
Damien Hirst- Contemporary Art YBA
Monet- Modern Art Impressionist
Banksy- Contemporary Art Graffiti Artist