What is the difference between non-objective and abstract? 

Non-objective sculpture or painting makes no intentional reference to any specific object and is appreciated and designed for its use of shape, space, line, form, texture, color, and value. ( elements of art) and the way these elements create interesting movement, balance, rhythm, focal point, emphasis etc.....
Abstract sculpture or paintings may be inspired by objects in nature, from the figure ( figurative) and make general references to objects without being realistic. Both use the elements and principles of art to create interesting work.