What is the difference between system analyst and programmer software engineer?

A title is just a title and what the people do under those titles can differ from company to company, but in general, a computer programmer translates a design into an actual computer program. A computer analyst, or more commonly called a systems analyst or business analyst or software architect will analyze a company process and design a software package that will improve that process. The systems analysts are usually individuals that bridge the gap between the real world and the programming world. They can speak "both languages" by helping the computer programmers understand the business process and by helping the software users understand the computer programming process. The two titles are similar to the difference between a home builder and an architect.