It took me a bit of time to figure this one out. Marshall Cavendish is the publisher of both series. The new Math in Focus series is a classroom based series that utilizes the Singapore approach for grades K-5. Marshall Cavendish also publishes the Primary Mathematics series that we use in our guides and spans grades 1-6. The main difference is that one series is written for the classroom and the other series is written in a way that makes it work either in the classroom or in a setting other than the classroom (such as the home setting).
Another thing to note is that the math syllabus in Singapore undergoes updates, and the Math in Focus series is based on the newer syllabus. Both the new Math in Focus series and the Primary Mathematics series are used in many classrooms across the U.S. and around the world with very good results.

You can feel very good about using the Primary Mathematics series with your family, as it provides excellent preparation in higher level thinking and mental math based on the same philosophy used in Singapore for math (carried out in the primary grades through the publisher Marshall Cavendish).
At HOD, we are currently looking toward recommending the Discovering Mathematics series for use after completion of Singapore Primary Mathematics 6B. The Discovering Mathematics series is one series used in Singapore at some point during grades 7-11 (for four years) and is designed to come after Primary Mathematics 6B (or its equivalent), although there is a placement test for those coming from a different math program. It follows the new syllabus from Singapore as well.

There are currently 4 series (that I am aware of) for grades 7 on up from Singapore that are offered in the U.S. They are as follows: New Elementary Math, Discovering Mathematics, New Syllabus Math, and New Math Counts. Hope that helps!
Blessings,
Carrie