Happy and content are synonyms (see this definition, and look at the synonyms; click on content as well), but not exclusive synonyms. You can be happy without being content, and you can be content without being happy.
I lost my inveestment, which I was not happy about, but I was content that the con artist went to jail.
This demonstrates how the two adjectives differ. You can be happy without being content, too.
I'm happy that I was promoted, but I won't be content till they make me Vice President.
So in that sense they are different. Still, the title of the book you mention seems to be interested in them only insofar as they are synonyms, to reinforce the paradoxical and tautological nature of the expression. It seems to be saying "Be content with what happiness you have, and be happy with what contentment you have." Circular reasoning, used as a rhetorical device.