JSP (Jackson Structured Programming) was the first software development method that Michael Jackson developed. It is a program design method, and was described in his book Principles of Program Design. JSP covers the design of individual programs, but not systems.
JSD (Jackson System Development) was the second software development method that Michael Jackson developed. JSD is a system development method not just for individual programs, but for entire systems. JSD is most readily applicable to information systems, but it can easily be extended to the development of (for example) real-time embedded systems. JSD was described in his book System Development.
Problem Analysis or the Problem Frames Approach was the third software development method that Michael Jackson developed. It concerns itself with aspects of developing all kinds of software, not just information systems. It was first sketched described in his book Software Requirements and Specifications, and much more fully in the book Problem Frames.
Each of these methods covers a wider scope than the previous one, and builds on ideas that appeared, but were not fully developed, in the previous one. So there was a real evolution... one set of ideas evolved into another.