Modernism Vs Modern Art.

Greenberg's definition leans more towards the idea that modernism is the movement that is focused on how a painting can separate itself, and be apart from, the other arts--he focuses on the unique ability to contribute to the art and culture of the time. It is mean to create the illusion that the artwork IS the space, or IS the form that it's meant to portray. 

Modern art however seeks to not create that illusion, it is meant to be flat and viewed as such.