Modernism was a movement that rose to popularity in late 1800s that embodied the ideas that traditional life did not fit the changes occurring in the new industrialized era along with the acceptance of self-consciousness, whereas postmodernism is a rejection of the focus on self and more focus on a group consciousness, along with the exaltation of "low" culture. High culture being replaced with popular culture is one of the most obvious shifts from the modernism school of thought to the postmodernism.
Art and architecture have some of the best examples of these two different schools of thought. Picasso, whose style revolutionized what was considered art, is one of the most well-known artists of the modernism era. The Abteiberg Museum in Germany is a good example of postmodernism architecture because it doesn't follow the traditional patterns with it's angled roof and non-traditional building finishes.