If I understand Carl Rogers aright, psychotherapy for him was all about learning that very distinction. He described it in "A Process Conception of Psychotherapy" which later became a chapter in his 1961 book On Becoming a Person. It's long been one of my favorite books. A Google Books copy of it is available online here.

I also found a webpage that sounds like someone's counseling homework on that chapter. I hesitate to recommend it because quite unlike Rogers, the author manages to make the topic cloudier rather than clearer for me. Perhaps it's a concrete example of thinking about feelings instead of feeling them. Anyway here's the link: Questions to help elucidate Rogers' seven stages of personality change in psychotherapy
I don't see them as true opposites. When you're learning to ride a bicycle, falling over to the left isn't really the opposite of falling over to the right. Either one is the opposite of keeping your wheels under you and staying upright.