Idealized style in art is just that -- making art that depicts a human ideal. This type of art aims for perfection. If we are referring to an idealized painting of a woman, for example, the woman will have a perfect, ideal shape. She will be beautiful with beautiful features, a desirable appearance, etc. This type of art emphasizes perfect characteristics and features.
Naturalism or realism, on the other hand, aims to portray art exactly as it is. Art that subscribes to naturalism or realism doesn't shy away from showing imperfections. In this type of art, you may see a woman in her natural state, perhaps a little fat, perhaps with a crooked nose if that's what she has. There is no attempt to beautify or perfect appearance. It is presented in its natural form.
Before the 19th century, idealized art was the norm. After the 19th century, naturalism and realism movements in art became more dominant.
An example of realist work is Rembrandt's painting "Hendrickje."
Raphael's paintings are examples of idealized art.