One of the differences is the number of problems in a single class period. In this country we focus almost exclusively on answer-getting strategies, ways to find the right answer, and so we have maybe 15 practice problems or even 20 or 30 in one lesson, and the student just tries again and again to practice the same strategy. In Japan there's a single question per lesson and that allows students not only to practice how to solve the problem and get the answer, but get at some of the deeper mathematical ideas.
Elizabeth Green talking about the differences between the way math is taught in Japan and in the United States. The distinction between answer finding and problem solving rinds me of Dan Meyer's discussion of the types of problems he uses to encourage patient problem solving.