Harcourt Math is from Houghton Mifflin group that publishes textbooks. There are a few publishers (Pearsons, Glencore, Mcgraw Hill, etc..) and they publish as per State Education agency guidelines/common core standard which means 1st grader will have 1st grade Math book. They are not much different from one another. And Harcourt Math or other textbooks are pretty thick and the teacher usually never finishes the book.
Singapore Math is a little more advance than US. So, 2nd grade S'pore Math may be for 3rd grade US level. But, S'pore Math does not cover everything what the kids taught in US.
S'pore Math is short and concise (not a lot of drill) and my DD loves it. We supplemented her with S'pore Math when she was 6.
